Line element-less method (LEM) for beam torsion solution (truly no-mesh method)

In this paper a new numerical method for finding approximate solutions of the torsion problem is proposed. The method takes full advantage of the theory of analytic complex function. A new potential function directly in terms of shear stresses is proposed and expanded in the double-ended Laurent series involving harmonic polynomials. A novel element-free weak form procedure, labelled Line Element-Less Method (LEM), has been developed imposing that the square of the net flux across the border is minimum with respect to coefficients expansion. Numerical implementation of the LEM results in systems of linear algebraic equations involving symmetric and positive-definite matrices without resorti…

An extended version of CVBEM method for solving shear problems

A Novel Mathematical Model For TLCD: Theoretical And Experimental Investigations

In this paper, a novel mathematical model for the Tuned Liquid Column Damper (TLCD) is presented. Taking advantages of fractional derivatives and related concepts, a new equation of motion of the liquid inside the TLCD is obtained. Experimental laboratory tests have been performed in order to validate the proposed linear fractional formulation. Comparison among experimental results, numerical obtained using the classical formulation and numerical with the new linear fractional formulation are reported. Results in frequency domain show how the new linear fractional formulation can predict the real behavior of such a passive vibration control system, more correctly than the classical mathemat…

Direct Derivation of Corrective Terms in SDE Through Nonlinear Transformation on Fokker–Planck Equation

This paper examines the problem of probabilistic characterization of nonlinear systems driven by normal and Poissonian white noise. By means of classical nonlinear transformation the stochastic differential equation driven by external input is transformed into a parametric-type stochastic differential equation. Such equations are commonly handled with Ito-type stochastic differential equations and Ito's rule is used to find the response statistics. Here a different approach is proposed, which mainly consists in transforming the Fokker–Planck equation for the original system driven by external input, in the transformed probability density function of the new state variable. It will be shown …

Arbitrarily shaped plates analysis via Line Element-Less Method (LEM)

Abstract An innovative procedure is introduced for the analysis of arbitrarily shaped thin plates with various boundary conditions and under generic transverse loading conditions. Framed into Line Element-less Method, a truly meshfree method, this novel approach yields the solution in terms of the deflection function in a straightforward manner, without resorting to any discretization, neither in the domain nor on the boundary. Specifically, expressing the deflection function through a series expansion in terms of harmonic polynomials, it is shown that the proposed method requires only the evaluation of line integrals along the boundary parametric equation. Further, minimization of appropri…

Probabilistic characterization of nonlinear systems under Poisson white noise parametric input via complex fractional moments

In this paper the probabilistic characterization of a nonlinear system enforced by parametric Poissonian white noise in terms of complex fractional moments is presented. In fact the initial system driven by a parametric input could be transformed into a system with an external type of excitation through an invertible nonlinear transformation. It is shown that by using Mellin transform theorem and related concepts, the solution of the Kolmogorov-Feller equation for the system with external input may be obtained in a very easy way.

Laplace’s Method of Integration in the Path Integral Approach for the Probabilistic Response of Nonlinear Systems

In this paper the response of nonlinear systems under stationary Gaussian white noise excitation is studied. The Path Integral (PI) approach, generally employed for evaluating the response Probability Density Function (PDF) of systems in short time steps based on the Chapman-Kolmogorov equation, is here used in conjunction with the Laplace’s method of integration. This yields an approximate analytical solution of the integral involved in the Chapman-Kolmogorov equation. Further, in this manner the repetitive integrations, generally required in the conventional numerical implementation of the procedure, can be circumvented. Application to a nonlinear system is considered, and pertinent compa…

A numerical model for pre-monitoring design of historical colonnade courtyards: The case study of chiaramonte palace in palermo

This paper proposes a numerical model that can be used for theoretical and experimental dynamic characterization of historical colonnade courtyards. Such an architectural element appears often in buildings of historical heritage and, especially under seismic excitation, it represents the most vulnerable structural part. Therefore, it is very important to have reliable as well as simple models available for vulnerability analysis, to evaluate different reinforcing systems if needed, or to plan dynamic characterization tests or monitoring campaigns, as in the present case. Chiaramonte Palace, a wonderful example of the historical heritage of Palermo, is investigated as case study. Firstly, a …

Bending test for capturing the fractional visco-elastic parameters: theoretical and experimental investigation on giant reeds

In this paper attention is devoted on searching a proper model for characterizing the behavior of giant reeds. To aim at this, firstly, meticulous experimental tests have been performed in the Laboratory of structural materials of University of Palermo. Further, the novel aspect of this paper is that of using an advanced Euler-Bernoulli model to fit experimental data of bending tests. Such a model of continuum beam takes into account different constitutive laws of visco-elasticity, being real materials visco-elastic.

Innovative modeling of tuned liquid column damper controlled structures

In this paper a different formulation for the response of structural systems controlled by Tuned Liquid Column Damper (TLCD) devices is developed, based on the mathematical tool of fractional calculus. Although the increasing use of these devices for structural vibration control, it has been demonstrated that existing model may lead to inaccurate prediction of liquid motion, thus reflecting in a possible imprecise description of the structural response. For this reason the recently proposed fractional formulation introduced to model liquid displacements in TLCD devices, is here extended to deal with TLCD controlled structures under base excitations. As demonstrated through an extensive expe…

Inverse Mellin Transform to characterize the nonlinear system PDF response to Poisson white noise

Multiplicative cases from additive cases: Extension of Kolmogorov–Feller equation to parametric Poisson white noise processes

Abstract In this paper the response of nonlinear systems driven by parametric Poissonian white noise is examined. As is well known, the response sample function or the response statistics of a system driven by external white noise processes is completely defined. Starting from the system driven by external white noise processes, when an invertible nonlinear transformation is applied, the transformed system in the new state variable is driven by a parametric type excitation. So this latter artificial system may be used as a tool to find out the proper solution to solve systems driven by parametric white noises. In fact, solving this new system, being the nonlinear transformation invertible, …

Poisson white noise parametric input and response by using complex fractional moments

Abstract In this paper the solution of the generalization of the Kolmogorov–Feller equation to the case of parametric input is treated. The solution is obtained by using complex Mellin transform and complex fractional moments. Applying an invertible nonlinear transformation, it is possible to convert the original system into an artificial one driven by an external Poisson white noise process. Then, the problem of finding the evolution of the probability density function (PDF) for nonlinear systems driven by parametric non-normal white noise process may be addressed in determining the PDF evolution of a corresponding artificial system with external type of loading.

Nonlinear vibrations of elastic beams with external general visco-elastic devices

Vibration damping for slender beams is achieved by applying devices at external points. The latter consist of general single visco-elastic springpot elements. An approximate nonlinear boundary value problem is found in frequency domain that holds for moderately large vibrations or for linear beams with external nonlinear devices, both in the vicinity of primary resonances. The interaction force of a so-called springpot element is expressed as a sum of two separate forces: the first develops due to the external loading function at the device location, and the second contribution arises due to an imposed time-harmonic support excitation with no other external forces acting on the structure. F…

Damage detection based on the analytical signal representation

Earthquake ground motion artificial simulations through Fractional Tajimi-Kanai Model

Non-linear systems under parametric alpha-stable LÉVY WHITE NOISES

In this study stochastic analysis of nonlinear dynamical systems under a-stable, multiplicative white noise has been performed. Analysis has been conducted by means of the Ito rule extended to the case of α-stable noises. In this context the order of increments of Levy process has been evaluated and differential equations ruling the evolutions of statistical moments of either parametrically and external dynamical systems have been obtained. The extended Ito rule has also been used to yield the differential equation ruling the evolution of the characteristic function for parametrically excited dynamical systems. The Fourier transform of the characteristic function, namely the probability den…

CVBEM solution for De Saint-Venant orthotropic beams under coupled bending and torsion

The aim of this paper is to provide a solution for the coupled flexure–torsion De Saint Venant problem for orthotropic beams taking full advantage of the complex variable boundary element method (CVBEM) properly extended using a complex potential function whose real and imaginary parts are related to the shear stress components, the orthotropic ratio and the Poisson coefficients. The proposed method returns the complete stress field and the unitary twist rotation of the cross section at once by performing only line integrals. Numerical applications have been reported to show the validity and the efficiency of the proposed modified CVBEM to handle shear stress problems in the presence of ort…

Fractional visco-elastic Euler–Bernoulli beam

Abstract Aim of this paper is the response evaluation of fractional visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads. Starting from the local fractional visco-elastic relationship between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is shown that, for homogeneous beam both correspondence principles also hold in the case of Euler–Bernoulli beam with fractional constitutive law. Virtual work principle is also derived and applied to some c…

Evaluation of Deflection of a Plate using Line Integrals

Rollio delle navi in presenza di onde modellate come processi gaussiani e poissoniani agenti simultaneamente.

Obiettivo del presente lavoro è l’estensione del metodo della path integral solution (PIS) per lo studio della dinamica del rollio delle navi in presenza di onde modellate come processi gaussiani e poissionani agenti simultaneamente. Si è proceduto dapprima a mostrare come la PIS consenta di valutare l’evoluzione temporale della funzione densità di probabilità (PDF) del processo di risposta, applicando il metodo ad equazioni differenziali stocastiche soggette a forzanti esterne gaussiane e poissoniane. Successivamente si è trattato il caso di un sistema non lineare soggetto ad entrambi i rumori gaussiano e poissoniano agenti contestualmente. Si è infine affrontato sia analiticamente che num…

Fractional viscoelastic beam under torsion

Abstract This paper introduces a study on twisted viscoelastic beams, having considered fractional calculus to capture the viscoelastic behaviour. Further another novelty of this paper is extending a recent numerical approach, labelled line elementless method (LEM), to viscoelastic beams. The latter does not require any discretization neither in the domain nor in the boundary. Some numerical applications have been reported to demonstrate the efficiency and accuracy of the method.

Comparison among three boundary element methods for torsion problems: CPM, CVBEM, LEM

This paper provides solutions for De Saint-Venant torsion problem on a beam with arbitrary and uniform cross-section. In particular three methods framed into complex analysis have been considered: Complex Polynomial Method (CPM), Complex Variable Boundary Element Method (CVBEM) and Line Element-less Method (LEM), recently proposed. CPM involves the expansion of a complex potential in Taylor series, computing the unknown coefficients by means of collocation points on the boundary. CVBEM takes advantage of Cauchy’s integral formula that returns the solution of Laplace equation when mixed boundary conditions on both real and imaginary parts of the complex potential are known. LEM introduces th…

Analysis of block random rocking on nonlinear flexible foundation

Abstract In this paper the rocking response of a rigid block randomly excited at its foundation is examined. A nonlinear flexible foundation model is considered accounting for the possibility of uplifting in the case of strong excitation. Specifically, based on an appropriate nonlinear impact force model, the foundation is treated as a bed of continuously distributed springs in parallel with nonlinear dampers. The statistics of the rocking response is examined by an analytical procedure which involves a combination of static condensation and stochastic linearization methods. In this manner, repeated numerical integration of the highly nonlinear differential equations of motion is circumvent…

Impulsive Tests on Historical Structures: The Dome of Teatro Massimo in Palermo

Cultural heritage is the set of things, that having particular historical cultural and aesthetic are of public interest and constitute the wealth and civilization of a place and its people. Sharpen up methodologies aimed at safeguarding of monuments is crucial because the future may have in mind the historical past. Italy is a country that has invested heavily on its historical memory returned in large part by the historical building or the monuments. Furthermore, culture represents a fundamental indicator of the growth of the culture of a country. Consider a monitoring project of one of the most Impressive theater in the world, like “Teatro Massimo” in Palermo (Italy), means to add value t…

Fractional visco-elastic systems under normal white noise

In this paper an original method is presented to compute the stochastic response of singledegree- of-freedom structural systems with viscoelastic fractional damping. The key-idea stems from observing that, based on a few manipulations involving an appropriate change of variable and a discretization of the fractional derivative operator, the equation of motion can be reverted to a coupled linear system involving additional degrees of freedom, the number of which depends on the discretization adopted for the fractional derivative operator. The method applies for fractional damping of arbitrary order a (0 < α < 1). For most common input correlation functions, including a Gaussian white noise, …

Waves propagation in a fractional viscoelastic continuum

In this paper the analysis of waves scattering in a fractional-type viscoelastic material is analyzed. Such a material involves, in the constitutive equation, the presence of noninteger order derivatives of the strain filed yielding a memory-type behavior of the material model. The presence of such a term has been also justified experimentally reporting the relaxation modulus of polymeric materials, obtained from experimental test, that are well-fitted by a powerlaw of fractional order. Some numerical applications reporting the standing-waves condition of an 1D solid varying the fractional differentiation order has also been reported in the paper.

Numerical and experimental validation of a simplied formulation for the design of TLCD

PLA based biocomposites reinforced with Arundo donax fillers

Abstract In this work, for the first time, a natural and almost inexpensive filler obtained by grinding the culms of Arundo donax was used to prepare PLA based biocomposites. The composites were prepared by melt compounding PLA with A. donax filler (ADF). The influence of the content and size of ADF on the morphology and on the mechanical and thermal properties of PLA–ADF composites was evaluated. Moreover, ADF was extracted from composites to evaluate the effect of processing on morphology and dimensions of the incorporated filler. Furthermore, the experimental elastic moduli of the biocomposites have been fitted, employing two theoretical models, i.e., Hill and Halpin–Tsai. The results sh…

Fractional Tajimi–Kanai model for simulating earthquake ground motion

The ground acceleration is usually modeled as a filtered Gaussian process. The most common model is a Tajimi–Kanai (TK) filter that is a viscoelastic Kelvin–Voigt unit (a spring in parallel with a dashpot) carrying a mass excited by a white noise (acceleration at the bedrock). Based upon the observation that every real material exhibits a power law trend in the creep test, in this paper it is proposed the substitution of the purely viscous element in the Kelvin Voigt element with the so called springpot that is an element having an intermediate behavior between purely elastic (spring) and purely viscous (dashpot) behavior ruled by fractional operator. With this choice two main goals are rea…

Stochastic analysis of dynamical systems with delayed control forces

Abstract Reduction of structural vibration in actively controlled dynamical system is usually performed by means of convenient control forces dependent of the dynamic response. In this paper the existent studies will be extended to dynamical systems subjected to non-normal delta-correlated random process with delayed control forces. Taylor series expansion of the control forces has been introduced and the statistics of the dynamical response have been obtained by means of the extended Ito differential rule. Numerical application provided shows the capabilities of the proposed method to analyze stochastic dynamic systems with delayed actions under delta-correlated process contrasting statist…

Steady-state dynamic response of various hysteretic systems endowed with fractional derivative elements

In this paper, the steady-state dynamic response of hysteretic oscillators comprising fractional derivative elements and subjected to harmonic excitation is examined. Notably, this problem may arise in several circumstances, as for instance, when structures which inherently exhibit hysteretic behavior are supplemented with dampers or isolators often modeled by employing fractional terms. The amplitude of the steady-state response is determined analytically by using an equivalent linearization approach. The procedure yields an equivalent linear system with stiffness and damping coefficients which are related to the amplitude of the response, but also, to the order of the fractional derivativ…

Smartphone-based bridge monitoring through vehicle-bridge interaction: analysis and experimental assessment

AbstractIn this study, the results of a vast experimental campaign on the applicability of a smartphone-based technique for bridge monitoring are presented. Specifically, the vehicle–bridge interaction (VBI)-based approach is exploited as a cost-effective means to estimate the natural frequencies of bridges, with the final aim of possibly developing low-cost and diffused infrastructure monitoring system. The analysis is performed using a common hybrid vehicle, fully equipped with classical piezoelectric accelerometers and a smartphone MEMS accelerometer, to record its vertical accelerations while passing over the bridge. In this regard, the experimental campaign is carried out considering t…

The moment equation closure method revisited through the use of complex fractional moments

In this paper the solution of the Fokker Planck (FPK) equation in terms of (complex) fractional moments is presented. It is shown that by using concepts coming from fractional calculus, complex Mellin transform and related ones the probability density function response of nonlinear systems may be written in discretized form in terms of complex fractional moment not requiring a closure scheme.

Flexural vibrations of discontinuous layered elastically bonded beams

Abstract This paper addresses the dynamic flexural behavior of layered elastically bonded beams carrying an arbitrary number of elastic translational supports and rotational joints. The beams are referred to as discontinuous for the discontinuities of response variables at the application points of supports/joints. The Euler-Bernoulli hypothesis is assumed to hold for each layer separately, and a linear constitutive relation between the horizontal interlayer slip and the interlaminar shear force is considered. Based on the theory of generalized functions to handle the discontinuities of response variables due to supports/joints, exact beam modes are obtained from a characteristic equation b…

Fluid-structure interaction and flow redistribution in membrane-bounded channels

The hydrodynamics of electrodialysis and reverse electrodialysis is commonly studied by neglecting membrane deformation caused by transmembrane pressure (TMP). However, large frictional pressure drops and differences in fluid velocity or physical properties in adjacent channels may lead to significant TMP values. In previous works, we conducted one-way coupled structural-CFD simulations at the scale of one periodic unit of a profiled membrane/channel assembly and computed its deformation and frictional characteristics as functions of TMP. In this work, a novel fluid&ndash

Higher order matrix differential equations with singular coefficient matrices

In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.

Complex fractional moments for the characterization of the probabilistic response of non-linear systems subjected to white noises

In this chapter the solution of Fokker-Planck-Kolmogorov type equations is pursued with the aid of Complex Fractional Moments (CFMs). These quantities are the generalization of the well-known integer-order moments and are obtained as Mellin transform of the Probability Density Function (PDF). From this point of view, the PDF can be seen as inverse Mellin transform of the CFMs, and it can be obtained through a limited number of CFMs. These CFMs’ capability allows to solve the Fokker-Planck-Kolmogorov equation governing the evolutionary PDF of non-linear systems forced by white noise with an elegant and efficient strategy. The main difference between this new approach and the other one based …

A Novel Solution to Find the Dynamic Response of an Euler–Bernoulli Beam Fitted with Intraspan TMDs under Poisson Type Loading

This contribution considers a virtual experiment on the vibrational response of rail and road bridges equipped with smart devices in the form of damping elements to mitigate vibrations. The internal damping of the bridge is considered a discontinuity that contain a dashpot. Exact complex eigenvalues and eigenfunctions are derived from a characteristic equation built as the determinant of a 4 x 4 matrix

An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems

The recently developed approximate Wiener path integral (WPI) technique for determining the stochastic response of nonlinear/hysteretic multi-degree-of-freedom (MDOF) systems has proven to be reliable and significantly more efficient than a Monte Carlo simulation (MCS) treatment of the problem for low-dimensional systems. Nevertheless, the standard implementation of the WPI technique can be computationally cumbersome for relatively high-dimensional MDOF systems. In this paper, a novel WPI technique formulation/implementation is developed by combining the “localization” capabilities of the WPI solution framework with an appropriately chosen expansion for approximating the system response PDF…

Direct evaluation of the equivalent linear damping for TLCD systems in random vibration for pre-design purposes

Abstract Passive control of structural vibrations has received in recent years a great attention from researchers concerned with vibration control. Several types of devices have been proposed in order to reduce the dynamic responses of different kinds of structural systems. Among them, the Tuned Liquid Column Damper (TLCD) proved to be very effective in reducing vibration of structures. Since the increasing use of TLCDs in practical realizations, this paper aims at developing an approximate formulation, by means of a statistical linearization technique, able to estimate the parameters of a structure equipped with a TLCD subjected to random loads for pre-design purposes. Moreover, it is show…

First-passage problem for nonlinear systems under Lévy white noise through path integral method

In this paper, the first-passage problem for nonlinear systems driven by $$\alpha $$ -stable Levy white noises is considered. The path integral solution (PIS) is adopted for determining the reliability function and first-passage time probability density function of nonlinear oscillators. Specifically, based on the properties of $$\alpha $$ -stable random variables and processes, PIS is extended to deal with Levy white noises with any value of the stability index $$\alpha $$ . Application to linear and nonlinear systems considering different values of $$\alpha $$ is reported. Comparisons with pertinent Monte Carlo simulation data demonstrate the accuracy of the results.

Stationary and non-stationary stochastic response of linear fractional viscoelastic systems

Abstract A method is presented to compute the stochastic response of single-degree-of-freedom (SDOF) structural systems with fractional derivative damping, subjected to stationary and non-stationary inputs. Based on a few manipulations involving an appropriate change of variable and a discretization of the fractional derivative operator, the equation of motion is reverted to a set of coupled linear equations involving additional degrees of freedom, the number of which depends on the discretization of the fractional derivative operator. As a result of the proposed variable transformation and discretization, the stochastic analysis becomes very straightforward and simple since, based on stand…

Active controlled structural systems under delta-correlated random excitation: linear and nonlinear case

Abstract Reduction of structural vibration in active controlled dynamical system is usually performed by means of convenient control forces dependent of the dynamic response. In this paper the existent studies will be extended to dynamical systems subjected to non-Gaussian random process accounting for the time delay involved in the application of active control actions. Control forces acting with time-delay effects will be expanded in Taylor series evaluating response statistics by means of the extended Ito differential rule to consider the effects of the non-normality of the input processes. Numerical application provided shows the feasibility of the proposed method to analyze stochastic …

Rocking of rigid block on nonlinear flexible foundation

Abstract The two prime models used currently to describe rocking of rigid bodies, the Housner’s model and the Winkler foundation model, can capture some of the salient features of the physics of this important problem. These two models involve either null or linear interaction between the block and the foundation. Hopefully, some additional aspects of the problem can be captured by an enhanced nonlinear model for the base-foundation interaction. In this regard, what it is adopted in this paper is the Hunt and Crossley’s nonlinear impact force model in which the impact/contact force is represented by springs in parallel with nonlinear dampers. In this regard, a proper mathematical formulatio…

Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral

A novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators endowed with fractional derivatives elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes which rely on a discrete version of the…

A novel method based on augmented Markov vector process for the time-variant extreme value distribution of stochastic dynamical systems enforced by Poisson white noise

Abstract The probability density function (PDF) of the time-variant extreme value process for structural responses is of great importance. Poisson white noise excitation occurs widely in practical engineering problems. The extreme value distribution of the response of systems excited by Poisson white noise processes is still not yet readily available. For this purpose, in the present paper, a novel method based on the augmented Markov vector process for the PDF of the time-variant extreme value process for a Poisson white noise driven dynamical system is proposed. Specifically, the augmented Markov vector (AMV) process is constructed by combining the extreme value process and its underlying…

Vibration-based identification of mechanical properties of orthotropic arbitrarily shaped plates: Numerical and experimental assessment

Abstract An innovative procedure is introduced for the identification of the mechanical parameters of orthotropic plates of arbitrary shape, under various boundary conditions, based on vibration data. The method employs a combination of a convenient Rayleigh-Ritz approach and Particle-Swarm Optimization to estimate elastic constants of the orthotropic material in a straightforward manner, without requiring computationally demanding iterative Finite Element analyses. Specifically, the pb-2 Rayleigh-Ritz procedure is extended and applied to deal with orthotropic plates, simplifying the approach to more easily treat generic plate shapes, taking advantage of the Green's theorem. The method is t…

α-stable distributions for better performance of ACO in detecting damage on not well spaced frequency systems

Abstract In this paper, the Ant Colony Optimization (ACO) algorithm is modified through α -stable Levy variables and applied to the identification of incipient damage in structural components. The main feature of the proposed optimization is an improved ability, which derives from the heavy tails of the stable random variable, to escape from local minima. This aspect is relevant since the objective function used for damage detection may have many local minima which render very challenging the search of the global minimum corresponding to the damage parameter. As the optimization is performed on the structural response and does not require the extraction of modal components, the method is pa…

Probabilistic response of nonlinear systems via PI: normal, Poissonian and combined white noises

A novel 2D model for the assessment of deformation-induced flow redistribution phenomena in electrodialysis units

Incipient damage identification through characteristics of the analytical signal response

The analytical signal is a complex representation of a time domain signal: the real part is the time domain signal itself, while the imaginary part is its Hilbert transform. It has been observed that damage, even at a very low level, yields clearly detectable variations of analytical signal quantities such as phase and instantaneous frequency. This observation can represent a step toward a quick and effective tool to recognize the presence of incipient damage where other frequency-based techniques fail. In this paper a damage identification procedure based on an adimensional functional of the square of the difference between the characteristics of the analytical theoretical and measured sig…

A damage identification procedure based on Hilbert transform: Experimental validation

SUMMARY This paper aims at validating the feasibility of an identification procedure, based on the use of the Hilbert transform, by means of experimental tests for shear-type multi-degree-of-freedom systems. Particularly, a three-degree-of-freedom frame will be studied either numerically or experimentally by means of a laboratory scale model built at the laboratory of the Structural, Aerospace and Geotechnical Engineering Department (DISAG) of University of Palermo. Several damage scenarios have been considered to prove the effectiveness of the procedure. Moreover, the experimental tests have been conducted by considering two different input loads: pulse forces, simulated by means of an ins…

Path Integral Solution Handled by Fractional Calculus

Implicit analytic solutions for a nonlinear fractional partial differential beam equation

Abstract Analytic solutions in implicit form are derived for a nonlinear partial differential equation (PDE) with fractional derivative elements, which can model the dynamics of a deterministically excited Euler-Bernoulli beam resting on a viscoelastic foundation. Specifically, the initial-boundary value problem for the corresponding PDE is reduced to an initial value problem for a nonlinear ordinary differential equation in a Hilbert space. Next, by employing the cosine and sine families of operators, a variation of parameters representation of the solution map is introduced. Due to the presence of a nonlinear term, a local fixed point theorem is employed to prove the local existence and u…

Random vibration TLCD controlled

Higher order matrix differential equations with singular coefficient matrices

In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.

Innovative modeling of Tuned Liquid Column Damper motion

Abstract In this paper a new model for the liquid motion within a Tuned Liquid Column Damper (TLCD) device is developed, based on the mathematical tool of fractional calculus. Although the increasing use of these devices for structural vibration control, it is shown that existing model does not always lead to accurate prediction of the liquid motion. A better model is then needed for accurate simulation of the behavior of TLCD systems. As regards, it has been demonstrated how correctly including the first linear liquid sloshing mode, through the equivalent mechanical analogy well established in literature, produces numerical results that highly match the corresponding experimental ones. Sin…

Analytical Solutions of Viscoelastic Nonlocal Timoshenko Beams

A consistent nonlocal viscoelastic beam model is proposed in this paper. Specifically, a Timoshenko bending problem, where size- and time-dependent effects cannot be neglected, is investigated. In order to inspect scale phenomena, a stress-driven nonlocal formulation is used, whereas to simulate time-dependent effects, fractional linear viscoelasticity is considered. These two approaches are adopted to develop a new Timoshenko bending model. Analytical solutions and application samples of the proposed formulation are presented. Moreover, in order to show influences of viscoelastic and size effects on mechanical response, parametric analyses are provided. The contributed results can be usefu…

Approximate analytical mean-square response of an impacting stochastic system oscillator with fractional damping

The paper deals with the stochastic dynamics of a vibroimpact single-degree-of-freedom system under a Gaussian white noise. The system is assumed to have a hard type impact against a one-sided motionless barrier, located at the system's equilibrium. The system is endowed with a fractional derivative element. An analytical expression for the system's mean squared response amplitude is presented and compared with the results of numerical simulations.

Non-stationary response of fractionally-damped viscoelastic systems

Optimal design of tuned liquid column damper inerter for vibration control

Abstract In this paper, the use of a novel passive control device defined as Tuned Liquid Column Damper Inerter (TLCDI) is studied to control the seismic response of structural systems. The TLCDI, recently introduced as an enhanced version of the conventional Tuned Liquid Column Damper, may achieve improved seismic performances by exploiting the mass amplification effect of the so-called inerter device. For this purpose, an optimization procedure for the design of the TLCDI based on a statistical linearization technique and the minimization of the structural displacement variance is proposed. Notably, by assuming a white noise base excitation and considering some additional approximations, …

Timoshenko vs Euler-Bernoulli beam: fractional visco-elastic behaviour

The Euler-Bernoulli beam theory is well established in such a way that engineers are very confident with the determination of stress field or def lections of the elastic beam based on this theory. Conversely Timoshenko theory is not so much used by engineers. However in such cases Euler-Bernoulli theory that n eglects the effect of transversal shear deformation leads to unacceptable results. For inst ance when dealing with the visco-elastic behaviour the shear deformations play a fundamental role. Recent studies [1]-[2] on the response evaluation of visco-elastic Euler-Bernoulli beam under quasi-static and dynamic loads, have been stressed that for better capturing the visco-elastic behavio…

A Non-stationary Fractional Tajimi Kanai Model of Earthquake Ground Motions

Misura delle vibrazioni sul simulacro argenteo dell'Immacolata processione

LEM for twisted re-entrant angle sections

In this paper an innovative numerical method named as line element-less method, LEM, for finding solution of torsion problem has been extended to all shaped sections, including sections possessing re-entrant angles at their boundary. The response solution in terms of shear stress field or Prandtl function or warping function in all domain and for any kind of domain with arbitrary contour, may be performed quickly, calculating line integrals only. The method takes full advantage of the theory of analytic complex function and is robust in the sense that returns exact solution if this exists. Numerical implementation of LEM has been developed using Mathematica software without resorting to any…

Direct evaluation of jumps for nonlinear systems under external and multiplicative impulses

In this paper the problem of the response evaluation of nonlinear systems under multiplicative impulsive input is treated. Such systems exhibit a jump at each impulse occurrence, whose value cannot be predicted through the classical differential calculus. In this context here the correct jump evaluation of nonlinear systems is obtained in closed form for two general classes of nonlinear multiplicative functions. Analysis has been performed to show the different typical behaviors of the response, which in some cases could diverge or converge to zero instantaneously, depending on the amplitude of the Dirac's delta.

Non-linear systems under parametric a-stable Levý white noises

Simplified analytical solution for the optimal design of Tuned Mass Damper Inerter for base isolated structures

Abstract In this paper the use of the Tuned Mass Damper Inerter (TMDI) to control the response of base isolated structures under stochastic horizontal base acceleration is examined. Notably, the TMDI, recently introduced as a generalization of the classical Tuned Mass Damper, allows to achieve enhanced performance compared to the other passive vibration control devices. Thus, it represents an ideal alternative for reducing displacements of base isolated structures. To this aim, firstly a straightforward numerical approach is developed for the optimal design of this device considering a white noise base excitation. Further, a simplified analytical solution for the optimal design of TMDI para…

An efficient framework for the elasto-plastic reliability assessment of uncertain wind excited systems

Abstract In this paper a method to efficiently evaluate the reliability of elastic-perfectly plastic structures is proposed. The method is based on combining dynamic shakedown theory with Subset Simulation. In particular, focus is on describing the shakedown behavior of uncertain elasto-plastic systems driven by stochastic wind loads. The ability of the structure to shakedown is assumed as a limit state separating plastic collapse from a safe, if not elastic, state of the structure. The limit state is therefore evaluated in terms of a probabilistic load multiplier estimated through solving a series of linear programming problems posed in terms of the responses of the underlying linear elast…

An Innovative Ambient Identification Method

Ambient modal identification, also known as Operational Modal Analysis (OMA), aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., no initial excitation or known artificial excitation. This procedure for testing and/or monitoring historic buildings, is particularly attractive for civil engineers concerned with the safety of complex historic structures. However, since the external force is not recorded, the identification methods have to be more sophisticated and based on stochastic mechanics. In this context, this contribution will introduce an innovative ambient identification method based on appl…

Complex analysis for the solution of torsion problems: a comparison among three methods

A non-homogeneous Poisson based model for daily rainfall data

In this paper we report some results of the application of a new stochastic model applied to rainfall daily data. The Poisson models, characterized only by the expected rate of events (impulse occurrences, that is the mean number of impulses per unit time) and the assigned probability distribution of the phenomenon magnitude, do not take into consideration the datum regarding the duration of the occurrences, that is fundamental from a hydrological point of view. In order to describe the phenomenon in a way more adherent to its physical nature, we propose a new model simple and manageable. This model takes into account another random variable, representing the duration of the rainfall due to…

Membrane Deformation and Its Effects on Flow and Mass Transfer in the Electromembrane Processes

In the membrane processes, a trans-membrane pressure (TMP) may arise due to design features or operating conditions. In most applications, stacks for electrodialysis (ED) or reverse electrodialysis (RED) operate at low TMP (&lt

Random Vibrations of Uncertain Linearly Elastic Trusses

Stochastic dynamics of linear elastic trusses in presence of structural uncertainties (virtual distortion approach)

Structures involving uncertainties in material and/or in geometrical parameters are referred to as uncertain structures. Reliability analysis of such structures strongly depends on variation of parameters and probabilistic approach is often used to characterize structural uncertainties. In this paper dynamic analysis of linearly elastic system in presence of random parameter variations will be performed. In detail parameter fluctuations have been considered as inelastic, stress and parameter dependent superimposed strains. Analysis is then carried out via superposition principle accounting for response to external agencies and parameter dependent strains. Proposed method yields asymptotic s…

Experimental validation of a fractional model for creep/recovery testing of asphalt mixtures

Abstract Prediction of asphalt mixtures’ behavior during their service life is a challenge due to its complexity and sensitivity to environmental and loading conditions. It has been proved that, when subjected to loading conditions comparable with most pavement operating conditions, asphalt mixtures behave as linear visco-elastic (LVE) materials. Traditionally the LVE behavior of bituminous material is modeled via creep/recovery functions. In the past, several rheological models constituted by elastic and viscous elements arranged in series or in parallel (analogical models) have been proposed and specified for both bitumen and asphalt mixtures. The corresponding constitutive laws always in…

An extension of the fractional model for construction of asphalt binder master curve

Knowledge and prediction of viscoelastic behaviour of asphalt binder is of great interest in order to design asphalt mixtures for civil construction of road and airports with good performances. The capability of a fractional model – requiring a very limited number of parameters – to describe and predict the linear viscoelastic behaviour of asphalt binder subjected to sinusoidal oscillations is investigated. Experimental data of complex modulus, |G*|, and phase angle, δ, are used to validate the proposed constitutive model. Based on the proposed extension of a fractional model, complex modulus isotherms for a range of frequencies can be created simply starting from isochronals at frequency v…

Stochastic analysis of motorcycle dynamics

Off-road and racing motorcycles require a particular setup of the suspensions to improve the comfort and the safety of the rider, maintaining a continuous contact between the road and the motorcycle (by means of the tires). Further, because of the ground roughness, in the case of offroad motorcycle, suspensions usually experience extreme and erratic excursions (suspension stroke) in performing their function. In this regard, the adoption of nonlinear devices can, perhaps, limit both the acceleration experienced by the sprung mass and the excursions of the suspensions. This leads to the consideration of asymmetric nonlinearly-behaving suspensions. This option, however, induces the difficulty…

Path integral solution for nonlinear systems under parametric Poissonian white noise input

Abstract In this paper the problem of the response evaluation in terms of probability density function of nonlinear systems under parametric Poisson white noise is addressed. Specifically, extension of the Path Integral method to this kind of systems is introduced. Such systems exhibit a jump at each impulse occurrence, whose value is obtained in closed form considering two general classes of nonlinear multiplicative functions. Relying on the obtained closed form relation liking the impulses amplitude distribution and the corresponding jump response of the system, the Path Integral method is extended to deal with systems driven by parametric Poissonian white noise. Several numerical applica…

Approximate survival probability determination of hysteretic systems with fractional derivative elements

Abstract A Galerkin scheme-based approach is developed for determining the survival probability and first-passage probability of a randomly excited hysteretic systems endowed with fractional derivative elements. Specifically, by employing a combination of statistical linearization and of stochastic averaging, the amplitude of the system response is modeled as one-dimensional Markovian Process. In this manner the corresponding backward Kolmogorov equation which governs the evolution of the survival probability of the system is determined. An approximate solution of this equation is sought by employing a Galerkin scheme in which a convenient set of confluent hypergeometric functions is used a…

Probabilistic characterization of nonlinear systems under Poisson white noise via complex fractional moments

In this paper, the probabilistic characterization of a nonlinear system enforced by Poissonian white noise in terms of complex fractional moments (CFMs) is presented. The main advantage in using such quantities, instead of the integer moments, relies on the fact that, through the CFMs the probability density function (PDF) is restituted in the whole domain. In fact, the inverse Mellin transform returns the PDF by performing integration along the imaginary axis of the Mellin transform, while the real part remains fixed. This ensures that the PDF is restituted in the whole range with exception of the value in zero, in which singularities appear. It is shown that using Mellin transform theorem…

The Saint-Venant cylinder under shear forces: Harmonic polynomial solution

CVBEM application to a novel potential function providing stress field and twist rotation at once

AbstractIn this paper, complex variable boundary element method (CVBEM) is used for the solution of de Saint-Venant’s torsion problem in homogenous isotropic elastic beams with a generic cross section, considering a complex potential function related to the stress field. Generally, CVBEM, when used for torsion problems, leads to evaluation of the stress field divided by the twist rotation. The latter has been evaluated by performing a domain integral. In this paper, taking advantage of the aforementioned potential function, it is possible, by applying CVBEM, to evaluate the complete stress distribution and the twist rotation of the cross section and the torsional stiffness factor, performin…

Non-linear transformation on Kolmogorov-Feller equation

Analysis of Rectangular Orthotropic Membranes for Mechanical Properties Identification through Load-Displacement Data

In this paper, an innovative procedure is introduced for the identification of the mechanical properties of orthotropic membranes based on load-displacement data. To this end, novel functional forms of the displacement components for rectangular membranes are appropriately introduced. Unknown coefficients of these displacement functions are determined, minimizing the total potential energy of the membrane. The energy method is then combined with an optimization procedure to estimate the elastic constants of the membranes in a straightforward manner. Specifically, a genetic algorithm is used to minimize a properly defined objective function directly related to the sought mechanical propertie…

Sulla necessità dei termini correttivi per lo studio di sistemi non lineari sollecitati da processi parametrici Poissoniani

Path Integral Method for Nonlinear Systems Under Levy White Noise

In this paper, the probabilistic response of nonlinear systems driven by alpha-stable Lévy white noises is considered. The path integral solution is adopted for determining the evolution of the probability density function of nonlinear oscillators. Specifically, based on the properties of alpha-stable random variables and processes, the path integral solution is extended to deal with Lévy white noises input with any value of the stability index alpha. It is shown that at the limit when the time increments tend to zero, the Einstein–Smoluchowsky equation, governing the evolution of the response probability density function, is fully restored. Application to linear and nonlinear systems under…

Ito calculus extended to non-linear systems under alpha-stable Lévy white noise

Optimal tuning of tuned liquid column damper systems in random vibration by means of an approximate formulation

Passive control devices are often added to slender and flexible systems in order to increase their structural safety. Several types of devices have been proposed in order to reduce the dynamic responses of different kind of structural systems. Among them, the tuned liquid column damper (TLCD) proved to be very effective in reducing vibration of various type of structures by means of a combined action which involves the motion of the liquid mass within the tube. The restoring force, in particular, is produced by the force of gravity acting on the liquid and the damping effect is generated by the hydrodynamic head losses that arise during the motion of the liquid inside the TLCD. Since the in…

The TLCD Passive Control: Numerical Investigations vs. Experimental Results

Very recently the tuned liquid column damper (TLCD) is receiving an increasing interest from researchers concerned with vibration control, to be considered an alternative device with respect to the tuned mass damper (TMD), since the former has low cost, easy adjustment, flexible installation. However, in recent studies the authors [1] have pointed out that for TMD the analytical formulation provides results that are in good agreement with the experimental ones, while for TLCD it has been deducted that the analytical formulation needs further investigation. In fact using the classical formulation of the problem, numerical results are very different from the experimental results obtained by t…

Experimental dynamic analysis of elastic-plastic shear frames with secondary structures

Various experimental models are developed to study the influence of lightweight secondary structures on the dynamic response of elastic and elastic-plastic shear frames. Small-scale two-story model frames, with an elastic single-degree-of-freedom secondary structure attached, are considered for sinusoidal and random in-plane support excitation. Both elastic and elastic-plastic responses are recorded by varying the material properties of the columns of a distinguished floor. Parametric studies are performed by varying the secondary structure's fundamental frequency and damping. Experimental results are compared with those obtained by computational simulations. Experimental and numerical resu…

Probabilistic analysis of truss structures with uncertain parameters (virtual distortion method approach)

A new approach for probabilistic characterization of linear elastic redundant trusses with uncertainty on the various members subjected to deterministic loads acting on the nodes of the structure is presented. The method is based on the simple observation that variations of structural parameters are equivalent to superimposed strains on a reference structure depending on the axial forces on the elastic modulus of the original structure as well as on the uncertainty (virtual distortion method approach). Superposition principle may be applied to separate contribution to mechanical response due to external loads and parameter variations. Statically determinate trusses dealt with the proposed m…

Response determination of linear dynamical systems with singular matrices: A polynomial matrix theory approach

Abstract An approach is developed based on polynomial matrix theory for formulating the equations of motion and for determining the response of multi-degree-of-freedom (MDOF) linear dynamical systems with singular matrices and subject to linear constraints. This system modeling may appear for reasons such as utilizing redundant DOFs, and can be advantageous from a computational cost perspective, especially for complex (multi-body) systems. The herein developed approach can be construed as an alternative to the recently proposed methodology by Udwadia and coworkers, and has the significant advantage that it circumvents the use of pseudoinverses in determining the system response. In fact, ba…

A Further Insight on the Intrinsic Mode Function through Stochastic Analysis

Geometrical deviation of end-of-life parts as a consequence of reshaping by single point incremental forming

AbstractPutting in place circular economy strategies is an urgent challenge to face. In this scenario, manufacturing processes play a relevant role as efficient material reuse enabler. Scientists have to make an effort either to find new process or to rethink old process to reprocess end-of-life (EoL) component to recover both material and functions. In this paper, single point incremental forming (SPIF) process is used for reshaping sheet metal EoL components. The entire process chain was replicated including both deep drawing process (to imitate the end-of-life component) as well as SPIF operations (to obtain the reshaped components). The geometrical deviation as a consequence of SPIF ope…

Path integral method for first-passage probability determination of nonlinear systems under levy white noise

In this paper the problem of the first-passage probabilities determination of nonlinear systems under alpha-stable Lévy white noises is addressed. Based on the properties of alpha-stable random variables and processes, the Path Integral method is extended to deal with nonlinear systems driven by Lévy white noises with a generic value of the stability index alpha. Furthermore, the determination of reliability functions and first-passage time probability density functions is handled step-by-step through a modification of the Path Integral technique. Comparison with pertinent Monte Carlo simulation reveals the excellent accuracy of the proposed method.

A Wiener Path Integral Technique for Non-Stationary Response Determination of Nonlinear Oscillators with Fractional Derivative Elements

In this paper a novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators with fractional derivative elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes. In this manner, the analytical Wi…

Stochastic ship roll motion via path integral method

ABSTRACTThe response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple …

Exact and approximate analytical solutions for nonlocal nanoplates of arbitrary shapes in bending using the line element-less method

AbstractIn this study, an innovative procedure is presented for the analysis of the static behavior of plates at the micro and nano scale, with arbitrary shape and various boundary conditions. In this regard, the well-known Eringen’s nonlocal elasticity theory is used to appropriately model small length scale effects. The proposed mesh-free procedure, namely the Line Element-Less Method (LEM), only requires the evaluation of simple line integrals along the plate boundary parametric equation. Further, variations of appropriately introduced functionals eventually lead to a linear system of algebraic equations in terms of the expansion coefficients of the deflection function. Notably, the prop…

Damage identification by a modified Ant Colony Optimization for not well spaced frequency systems

Recently, it has been shown , that a damage detection strategy based on a proper functional calculated on the analytical signal of the structural dynamical response, consents to identify very low damage level. In this regard, they stressed the efficiency of Hilbert Transform to obtain the analytical response representation that shows more sensitivity for predicting damage with respect to the simple signal response. Then, a damage identification procedure based on the minimization of the difference between theoretical and measured data was proposed with satisfactory results. Unfortunately, this procedure, since the need of use of band pass filter around the natural frequency of the system, f…

A modified Ant Colony damage identification algorithm for not well spaced frequency systems

Damage identification is of primary concern in many fields of civil engineering. Usually the damage is detected from the variation of structural response induced. When the damage level is very low, incipient damage, this variation is hardly seen. In the present work is studied the case of not well spaced frequency systems. Identification problem is formulated as a minimum problem of a functional expressed in term of damage parameters. The minimum problem is solved by heuristic algorithm, ACORL.

The Fractionally-damped Duffing Oscillator under Gaussian white noise

Non-linear viscoelastic behavior of polymer melts interpreted by fractional viscoelastic model

Very recently, researchers dealing with constitutive law pertinent viscoelastic materials put forward the successful idea to introduce viscoelastic laws embedded with fractional calculus, relating the stress function to a real order derivative of the strain function. The latter consideration leads to represent both, relaxation and creep functions, through a power law function. In literature there are many papers in which the best fitting of the peculiar viscoelastic functions using a fractional model is performed. However there are not present studies about best fitting of relaxation function and/or creep function of materials that exhibit a non-linear viscoelastic behavior, as polymer melt…

Nonlinear rocking of rigid blocks on flexible foundation: Analysis and experiments

Abstract Primarily, two models are commonly used to describe rocking of rigid bodies; the Housner model, and the Winkler foundation model. The first deals with the motion of a rigid block rocking about its base corners on a rigid foundation. The second deals with the motion of a rigid block rocking and bouncing on a flexible foundation of distributed linear springs and dashpots (Winkler foundation). These models are two-dimensional and can capture some of the features of the physics of the problem. Clearly, there are additional aspects of the problem which may be captured by an enhanced nonlinear model for the base-foundation interaction. In this regard, what it is adopted in this paper is …

Stochastic dynamics of linear structures with nonlinear damper devices (PIS method)

Assessment of the tuned mass damper inerter for seismic response control of base‐isolated structures

In this paper, the hybrid control of structures subjected to seismic excitation by means of tuned mass damper inerter (TMDI) and base-isolation subsystems is studied with the aim of improving the dynamic performance of base-isolated structures by reducing the displacement demand of the isolation subsystem. The seismic performance of TMDI hybrid controlled structures is investigated in a comparative study, considering simple isolated systems and systems equipped with other absorber devices such as the tuned mass damper (TMD) and the tuned liquid column damper (TLCD). The TMDI has been optimized by performing a simplified approach based on minimizing the base-isolation subsystem displacement …

A fractionally-damped duffing oscillator driven by stochastic agencies

On the moving load problem in Euler–Bernoulli uniform beams with viscoelastic supports and joints

This paper concerns the vibration response under moving loads of Euler–Bernoulli uniform beams with translational supports and rotational joints, featuring Kelvin–Voigt viscoelastic behaviour. Using the theory of generalized functions to handle the discontinuities of the response variables at the support/joint locations, exact beam modes are obtained from a characteristic equation built as determinant of a (Formula presented.) matrix, for any number of supports/joints. Based on pertinent orthogonality conditions for the deflection modes, the response under moving loads is built in the time domain by modal superposition. Remarkably, all response variables are built in a closed analytical for…

Funzione densità di probabilità della risposta di strutture esposte al vento (PIS)

Vibration mitigation of the Silver Madonna during the procession in Palermo: preliminary study

Base-isolated structure equipped with tuned liquid column damper: An experimental study

Abstract In this study, a novel passive vibration control strategy is investigated experimentally, where a Tuned Liquid Column Damper protects a base-isolated structure. The Tuned Liquid Column Damper is attached to the base, in contrast to typical attachment points of passive energy dissipation devices in high-rise buildings at elevated levels. Experiments on a base-excited small-scale three-story shear frame are conducted in order to study effects of both control devices – base-isolation and Tuned Liquid Column Damper – on the structural model. The dynamic properties of the stand-alone shear frame and the base-isolation subsystem are derived using standard dynamic test methods based on di…

Generalized differential transform method for nonlinear boundary value problem of fractional order

Abstract In this paper the generalized differential transform method is applied to obtain an approximate solution of linear and nonlinear differential equation of fractional order with boundary conditions. Several numerical examples are considered and comparisons with the existing solution techniques are reported. Results show that the method is effective, easier to implement and very accurate when applied for the solution of fractional boundary values problems.

FRACTIONAL MOMENTS AND PATH INTEGRAL SOLUTION FOR NON LINEAR SYSTEMS DRIVEN BY NORMAL WHITE NOISE

Mechanically-based approach to non-local elasticity: Variational principles

Abstract The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Mo…

Low stiffness variation in structural systems: identification and localization

When a very low damage occurs, the undamaged structural response totally overlaps the damaged one either in time domain or in frequency domain; on the other hand, by considering some characteristics of the analytical signal, such as the phase, it has been possible to develop a damage identification procedure that allows the identification and localization of damage even if the structure experiences multiple damages at the same time. This procedure is also robust with respect to the presence of measuring noise. In order to assess the validity of the proposed damage identification procedure, numerical applications on single degree of freedom and 2 DOF and 4 DOF are presented using data record…

Random vibration mitigation of beams via tuned mass dampers with spring inertia effects

The dynamics of beams equipped with tuned mass dampers is of considerable interest in engineering applications. Here, the purpose is to introduce a comprehensive framework to address the stochastic response of the system under stationary and non-stationary loads, considering inertia effects along the spring of every tuned mass damper applied to the beam. For this, the key step is to show that a tuned mass damper with spring inertia effects can be reverted to an equivalent external support, whose reaction force on the beam depends only on the deflection of the attachment point. On this basis, a generalized function approach provides closed analytical expressions for frequency and impulse res…

Mechanical-fluid dynamics coupled model for profiled Ion Exchange Membranes design

In this work, we developed an advanced model useful for the design of profiled IEMs, based on the coupled simulation of local mechanical deformations and of fluid dynamics and associated mass transport phenomena within deformed channels

Time delay induced effects on control of non-linear systems under random excitation

Dynamic response of equivalent orthotropic plate model for stiffened plate: numerical-experimental assessment

Abstract Over the last two decades, homogenization-based modeling techniques have attracted considerable attention. In fact, through these methods, structures such as corrugated or stiffened plates, commonly referred to as structurally orthotropic plates, can be approximately studied as equivalent flat plates with orthotropic behavior. Specifically, these homogenization techniques allow for the direct determination of the equivalent flexural and torsional rigidities which appear in the governing equation for the deflection of the equivalent orthotropic plate. It is worth noting that, the determined equivalent material properties retain the dependence on the geometric parameters of the origi…

Bending test for capturing the vivid behavior of giant reeds, returned through a proper fractional visco-elastic model

Abstract This paper presents results of experimental investigations made to evaluate the vivid behavior of giant reed Arundo donax. In particular, attention was paid to the relationship between visco-elastic properties and moisture content, which is widely recognized as one of the key factor that influences the mechanical properties of all wood-based materials. To this aim, after a controlled drying treatment on samples of reed, stress relaxation tests in three point bending configuration were performed to evaluate the effects of moisture content on visco-elastic behavior of the giant reed. Further, the novel aspect of this paper is that of using an Euler–Bernoulli model embedded with an ad…

Smart structures through nontraditional design of Tuned Mass Damper Inerter for higher control of base isolated systems

Abstract This paper introduces a smart structure design through the definition of an innovative passive control strategy, referred to as New Tuned Mass Damper Inerter (New TMDI), coupled with a base isolation system (BI), to control displacements in base isolated structures under seismic excitations. The herein proposed New TMDI comprises a recently developed nontraditional Tuned Mass Damper (known as New TMD), in which a secondary mass system is connected to the base plate of the BI system by a spring and to the ground by a dashpot, and of an inerter device placed in parallel with the damper. An optimization procedure which minimizes the base displacement variance of the BI system, conside…

Optimal design of tuned liquid column dampers for seismic response control of base-isolated structures

In this paper, the use of a tuned liquid column damper (TLCD) as a cost-effective means to control the seismic response of a base-isolated structure is studied. A straightforward direct approach for the optimal design of such a device is proposed, considering a white noise model of the base excitation. On this base, a direct optimization procedure of the TLCD design parameters is performed and optimal design charts are presented as a ready-to-use practical design tool. Comparison with the optimal parameters obtained considering a classical iterative statistical linearization technique proves the reliability of the proposed approach. The performance of the base-isolated TLCD-controlled struc…

Conservation and Folklore: Monitoring the Statue of the Silver Madonna in Palermo

Extension of the line element-less method to dynamic problems

The line element-less method is an efficient approach for the approximate solution of the Laplace or biharmonic equation on a general bidimensional domain. Introducing generalized harmonic polynomials as approximation functions, we extend the line element-less method to the inhomogeneous Helmholtz equation and to the eigenvalue problem for the Helmholtz equation. The obtained approximate solutions are critically discussed and advantages as well as limitations of the approach are pointed out.

Stochastic response determination of structural systems modeled via dependent coordinates: a frequency domain treatment based on generalized modal analysis

Generalized independent coordinates are typically utilized within an analytical dynamics framework to model the motion of structural and mechanical engineering systems. Nevertheless, for complex systems, such as multi-body structures, an explicit formulation of the equations of motion by utilizing generalized, independent, coordinates can be a daunting task. In this regard, employing a set of redundant coordinates can facilitate the formulation of the governing dynamics equations. In this setting, however, standard response analysis techniques cannot be applied in a straightforward manner. For instance, defining and determining a transfer function within a frequency domain response analysis…

Path integral solution by fractional calculus

In this paper, the Path Integral solution is developed in terms of complex moments. The method is applied to nonlinear systems excited by normal white noise. Crucial point of the proposed procedure is the representation of the probability density of a random variable in terms of complex moments, recently proposed by the first two authors. Advantage of this procedure is that complex moments do not exhibit hierarchy. Extension of the proposed method to the study of multi degree of freedom systems is also discussed.

A 2-D model of electrodialysis stacks including the effects of membrane deformation

Abstract Membrane-based processes have gained a relevant role in many engineering applications. Much effort has been devoted to thoroughly understand the fundamental phenomena behind them. However, membrane deformation has been taken into consideration only recently, although much evidence has shown its impacts in many applications. This work presents a novel 2-D, multi-scale, semi-empirical process model able to predict the behavior and the performance of Electrodialysis (ED) systems in cross-flow configurations in the presence and absence of local membrane deformations. The model exploits the results and the simulation approaches of previous fluid-structure investigations performed by the…

An Innovative Structural Dynamic Identification Procedure Combining Time Domain OMA Technique and GA

In this paper an innovative and simple Operational Modal Analysis (OMA) method for structural dynamic identification is proposed. It combines the recently introduced Time Domain&ndash;Analytical Signal Method (TD&ndash;ASM) with the Genetic Algorithm (GA). Specifically, TD&ndash;ASM is firstly employed to estimate a subspace of candidate modal parameters, and then the GA is used to identify the structural parameters minimizing the fitness value returned by an appropriately introduced objective function. Notably, this method can be used to estimate structural parameters even for high damping ratios, and it also allows one to identify the Power Spectral Density (PSD) of the structural excitat…

Dynamic Finite Element analysis of fractionally damped structural systems in the time domain

Visco-elastic material models with fractional characteristics have been used for several decades. This paper provides a simple methodology for Finite-Element-based dynamic analysis of structural systems with viscosity characterized by fractional derivatives of the strains. In particular, a re-formulation of the well-known Newmark method taking into account fractional derivatives discretized via the Grunwald–Letnikov summation allows the analysis of structural systems using standard Finite Element technology.

Probabilistic response of nonlinear systems under combined normal and Poisson white noise via path integral method

In this paper the response in terms of probability density function of nonlinear systems under combined normal and Poisson white noise is considered. The problem is handled via a Path Integral Solution (PIS) that may be considered as a step-by-step solution technique in terms of probability density function. A nonlinear system under normal white noise, Poissonian white noise and under the superposition of normal and Poisson white noise is performed through PIS. The spectral counterpart of the PIS, ruling the evolution of the characteristic functions is also derived. It is shown that at the limit when the time step becomes an infinitesimal quantity an equation ruling the evolution of the pro…

CVBEM for solving De Saint-Venant solid under shear forces

Abstract Evaluation of shear stresses distribution due to external shear forces applied to De Saint-Venant beams has been solved through Complex Variable Boundary Element Method properly extended, to benefit from advantages of this method, so far widely used for twisted solids. Extending the above method, further simplifications have been introduced such as those of performing line integrals only, instead of domain integrals. Numerical applications confirm accuracy and efficiency of the proposed extended version of the method, since the good agreement with results proposed in literature.

Ship Roll Motion under Stochastic Agencies Using Path Integral Method

The response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple dynamica…

A novel identification procedure from ambient vibration data

AbstractAmbient vibration modal identification, also known as Operational Modal Analysis, aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., no initial excitation or known artificial excitation. This procedure for testing and/or monitoring historic buildings, is particularly attractive for civil engineers concerned with the safety of complex historic structures. However, since the external force is not recorded, the identification methods have to be more sophisticated and based on stochastic mechanics. In this context, this contribution will introduce an innovative ambient identification method b…

Design Of TLCD under random loads: a new formulation

On the Stochastic Response of a Fractionally-damped Duffing Oscillator

A numerical method is presented to compute the response of a viscoelastic Duffing oscillator with fractional derivative damping, subjected to a stochastic input. The key idea involves an appropriate discretization of the fractional derivative, based on a preliminary change of variable, that allows to approximate the original system by an equivalent system with additional degrees of freedom, the number of which depends on the discretization of the fractional derivative. Unlike the original system that, due to the presence of the fractional derivative, is governed by non-ordinary differential equations, the equivalent system is governed by ordinary differential equations that can be readily h…

Mechanical Behavior Of Fractional Visco-Elastic Beams

Modeling of the viscoelastic behavior of paving bitumen using fractional derivatives

The paving grade bitumen used in the production of asphalt mixtures for road construction is significantly able to affect the in-service performances of flexible road pavements. It has been proved that, when subjected to loading conditions comparable with most pavement operating conditions, bituminous binders behave as linear visco-elastic materials. The aim of this paper is to propose a model based on fractional differential equations which is able to describe the behavior of bituminous binders in the linear viscoelastic range. Shear creep testing and creep recovery testing were carried out over a range of temperatures and by applying a stress level which makes it possible to maintain the …

Stochastic response of fractional visco-elastic beams

Stochastic response of a fractional vibroimpact system

Abstract The paper proposes a method to investigate the stochastic dynamics of a vibroimpact single-degree-of-freedom fractional system under a Gaussian white noise input. It is assumed that the system has a hard type impact against a one-sided motionless barrier, which is located at the system’s equilibrium position; furthermore, the system under study is endowed with an element modeled with fractional derivative. The proposed method is based on stochastic averaging technique and overcome the particular difficulty due to the presence of fractional derivative of an absolute value function; particularly an analytical expression for the system’s mean squared response amplitude is presented an…

The mechanically based non-local elasticity: an overview of main results and future challenges

The mechanically based non-local elasticity has been used, recently, in wider and wider engineering applications involving small-size devices and/or materials with marked microstructures. The key feature of the model involves the presence of non-local effects as additional body forces acting on material masses and depending on their relative displacements. An overview of the main results of the theory is reported in this paper.

Fractional models for capturing both relaxation and creep phase

Non-linear systems under Levy White Noise Handled by path integration method

Aim of this paper is an investigation on the consistency of the Path Integration (PI) method already proposed by Naess & Johansen, 1991,1993 for non-linear systems driven by α-stable white noise. It is shown that in the limit, as τ→0, the Einstein-Smoluchowsky (ES) equation is fully restored. Once the consistency of the PI is demonstrated for the half oscillator, then the extension of the ES equation for MDOF system is found starting from the PI method.

On an approximate solution of fractionally damped dynamical systems

Innovative straight formulation for plate in bending

In this paper it has been introduced an innovative formulation for evaluating the deflection function of a simply supported plate loaded by uniformly distributed edge moments. Framed into Line Element-less Method, this formulation allows the evaluation of solution in terms of deflection, through few lines of algorithm implemented by Mathematica software without resorting to any discretization neither in the domain nor in the boundary. Interesting savings in terms of time and computational costs are achieved. Results obtained by the proposed method are well contrasted by ones obtained by classical methods and Finite Element Method.

Direct evaluation of the equivalent linear damping for Tuned Liquid Column Damper systems in random vibration for pre-design purposes

Experimental validation of a direct pre-design formula for TLCD

The passive control of vibrations has received in recent years a great deal of attention from researchers. Several types of devices have been proposed in order to reduce the dynamic responses of different kinds of structural systems. Among them, the Tuned Liquid Column Damper (TLCD) has proved to be very effective in reducing vibration of structures. However, since the equations governing the TLCD controlled systems response is nonlinear, the calibration of TLCD parameters is time consuming and not convenient to perform in a pre-design phase. In this context, it has recently been introduced by the authors a formula that allows to choose the optimal parameters of TLCD in a direct and fast wa…

Truly no-mesh method for beam torsion solution

Itô calculus extended to systems driven by -stable Lévy white noises (a novel clip on the tails of Lévy motion)

Abstract The paper deals with probabilistic characterization of the response of non-linear systems under α -stable Levy white noise input. It is shown that, by properly selecting a clip in the probability density function of the input, the moments of the increments of Levy motion process remain all of the same order ( d t ) , like the increments of the Compound Poisson process. It follows that the Ito calculus extended to Poissonian input, may also be used for α -stable Levy white noise input processes. It is also shown that, when the clip on the tails of the probability of the increments of the Levy motion approaches to infinity, the Einstein–Smoluchowsky equation is restored. Once these c…

Theoretical and experimental analysis of viscoelastic behavior of biomaterials

Damage identification by Lévy ant colony optimization

This paper deals with the identification of incipient damage in structural elements by non-destructive test based on experimentally measured structural dynamical response. By applycation of the Hilbert transform to the recorded signal the so-called phase of the analytical signal is recovered and a proper functional is constructed in such a way that its global minimum gives a measure of the damage level, meant as stiffness reduction. Minimization is achieved by applying a modified Ant Colony Optimization (ACO) for continuous variables, inspired by the ants’ forageing behavior. The modification consists in the application of a new perturbation operator, based on alpha stable Lévy distribution…

Probabilistic response of linear structures equipped with nonlinear damper devices (PIS method)

Passive control introducing energy absorbing devices into the structure has received considerable attention in recent years. Unfortunately the constitutive law of viscous fluid dampers is highly nonlinear, and even supposing that the structure behaves linearly, the whole system has inherent nonlinear properties. Usually the analysis is performed by a stochastic linearization technique (SLT) determining a linear system equivalent to the nonlinear one, in a statistical sense. In this paper the effect of the non-Gaussianity of the response due to the inherent nonlinearity of the damper device will be studied in detail via the Path Integral Solution (PIS) method. A systematic study is conducted…

Probabilistic characterization of nonlinear systems under parametric Poisson white noise via complex fractional moments

Probabilistic response of linear structures equipped with nonlinear dampers devices (PIS method)

Passive control introducing energy absorbing devices into the structure has received considerable attention in recent years. Unfortunately the constitutive law of viscous fluid dampers is highly nonlinear, and even supposing that the structure behaves linearly, the whole system has inherent nonlinear properties. Usually the analysis is performed by a stochastic linearization technique (SLT) determining a linear system equivalent to the nonlinear one, in a statistical sense. In this paper the effect of the non-Gaussianity of the response due to the inherent nonlinearity of the damper device will be studied in detail via the Path Integral Solution (PIS) method. A systematic study is conducted…

Fractional visco-elastic Timoshenko beam from elastic Euler-Bernoulli beam

The Euler–Bernoulli beam theory is well established in such a way that engineers are very confident with the determination of the stress field or deflections of the elastic beam based on this theory. In contrast, Timoshenko theory is not so much used by engineers. However, in some cases, Euler–Bernoulli theory, which neglects the effect of transversal shear deformation, yields unacceptable results. For instance, when dealing with visco-elastic behavior, shear deformations play a fundamental role. Recent studies on the response evaluation of a visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads have been stressed that for better capturing of the visco-elastic behavior, a …

On the moving multi-loads problem in discontinuous beam structures with interlayer slip

Abstract This contribution proposes an efficient approach to the moving multi-loads problem on two-layer beams with interlayer slip and elastic translational supports. The Euler-Bernoulli hypothesis is assumed to hold for each layer separately, and a linear constitutive relation between the horizontal slip and the interlaminar shear force is considered. It is shown that, using the theory of generalized functions to treat the discontinuous response variables, exact eigenfunctions can be derived from a characteristic equation built as determinant of a 6 x 6 matrix. Building pertinent orthogonality conditions for the deflection eigenfunctions, a closed-form analytical response is established i…

A novel fluid-structure 2D modelling tool for the assessment of membrane deformation effects on electrodialysis units performances

Fractional visco-elastic Timoshenko beam deflection via single equation

SUMMARY This paper deals with the response determination of a visco-elastic Timoshenko beam under static loading condition and taking into account fractional calculus. In particular, the fractional derivative terms arise from representing constitutive behavior of the visco-elastic material. Further, taking advantages of the Mellin transform method recently developed for the solution of fractional differential equation, the problem of fractional Timoshenko beam model is assessed in time domain without invoking the Laplace-transforms as usual. Further, solution provided by the Mellin transform procedure will be compared with classical Central Difference scheme one, based on the Grunwald–Letni…

Self-similarity and response of fractional differential equations under white noise input

Self-similarity, fractal behaviour and long-range dependence are observed in various branches of physical, biological, geological, socioeconomics and mechanical systems. Self-similarity, also termed self-affinity, is a concept that links the properties of a phenomenon at a certain scale with the same properties at different time scales as it happens in fractal geometry. The fractional Brownian motion (fBm), i.e. the Riemann-Liouville fractional integral of the Gaussian white noise, is self-similar; in fact by changing the temporal scale t -&gt; at (a &gt; 0), the statistics in the new time axis (at) remain proportional to those calculated in the previous axis (t). The proportionality coeffi…

Vibrations of elastic structures with external nonlinear visco-elastic damping devices

Non-linear systems under impulsive parametric input

In this paper the problem of the response of non-linear systems excited by an impulsive parametric input is treated. For such systems the response exhibits a jump depending on the amplitude of the impulse as well as on the value of the state variables immediately before the impulse occurrence. Recently, the jump prediction has been obtained in a series form. Here the incremental rule for any scalar real valued function is obtained in an analytical form involving the jump of the state variables. It is also shown that the formulation for the jump evaluation is also able to give a new step-by-step integration technique.

Non-linear systems under delta correlated processes handled by perturbation theory

Statistical responses in terms of moment and correlation functions of non-linear systems driven by non-normal delta correlated external pulses are derived. The procedure takes full advantage of the perturbation theory approach. Then, by means of a proper coordinate transformation, the system is replaced by a quasi-linear system for which the statistical quantities can be exactly found.

Fractional visco-elastic Timoshenko beam deflection via single equation

This paper deals with the response determination of a visco-elastic Timoshenko beam under static loading condition and taking into account fractional calculus. In particular, the fractional derivative terms arise from representing constitutive behavior of the visco-elastic material. Further, taking advantages of the Mellin transform method recently developed for the solution of fractional differential equation, the problem of fractional Timoshenko beam model is assessed in time domain without invoking the Laplace-transforms as usual. Further, solution provided by the Mellin transform procedure will be compared with classical Central Difference scheme one, based on the Grunwald-Letnikov appr…

Stochastic analysis of linear and nonlinear systems under α-stable Lèvy white noise

On the moving load problem in beam structures equipped with tuned mass dampers

This paper proposes an original and efficient approach to the moving load problem on Euler–Bernoulli beams, with Kelvin–Voigt viscoelastic translational supports and rotational joints, and in addition, equipped with Kelvin–Voigt viscoelastic tuned mass dampers (TMDs). While supports are taken as representative of external devices such as grounded dampers or in-span supports with flexibility and damping, the rotational joints may model rotational dampers or connections with flexibility and damping arising from imperfections or damage. The theory of generalised functions is used to treat the discontinuities of the response variables, which involves deriving exact complex eigenvalues and eigen…

Earthquake Excited Base-Isolated Structures Protected by Tuned Liquid Column Dampers: Design Approach and Experimental Verification

Abstract In this contribution a direct approach for optimal design of a Tuned Liquid Column Damper (TLCD) device attached to the base slab of a base-isolated structure is presented, aiming at reducing the seismic displacement demand of the base-isolation subsystem. Assuming white noise base excitation, for a wide parameter range a direct optimization procedure yields design charts for optimal TLCD quantities. The performance of the base-isolated structure equipped with optimally tuned TLCD device in comparison to the simple base-isolated one is evaluated both numerically and experimentally. In a numerical study the system is subjected to the 44 records of the FEMA P-695 far-field ground mot…

Identification of Bending Modes of Vibration in Rails by a Laser Doppler Vibrometer on a Moving Platform

This paper introduces a method to identify the bending modes of vibration of railway tracks by using a laser Doppler vibrometer (LDV) mounted on a moving platform. Two sets of experiments were conducted at Transportation Technology Center Inc. (TTCI) in Pueblo Colorado, in order to validate the proposed method. First, the bending vibration modes were identified using the signals collected from a rail span (rail section between two consecutive sleepers) by accelerometers under moving car excitation. Then, vibration measurements from rail spans were obtained by using an LDV mounted on the moving railcar. All tests were carried out at four different rail car speeds: 8 km/h (5 mph), 16 km/h (10…

The fractional tajimi-kanai model of earthquake gound motion

Nontraditional configuration of tuned liquid column damper inerter for base-isolated structures

In this paper, the concept of a novel passive control device, namely the Nontraditional Tuned Liquid Column Damper Inerter (NT-TLCDI), is investigated in combination with seismic base isolation (BI), to control lateral displacement demands in base-isolated structures during seismic events. The considered NT-TLCDI is a revision of the ordinary configuration of the recently proposed Tuned Liquid Column Damper Inerter (TLCDI). Unlike the traditional TLCDI layout, which involves a secondary liquid mass in a U-shaped tank coupled with a grounded inerter and connected to the isolation system by a spring-dashpot system, in the NT-TLCDI configuration, the damper is in parallel with the inerter rath…

Nonlinear vibrations of elastic beams with external general visco-elastic devices

Non-linear systems under parametric white noise input: digital simulation and response

Abstract Monte Carlo technique is constituted of three steps. Therefore, improving such technique in practice means, improving the procedure used in one of the three following steps: (i) sample paths of the stochastic input process, (ii) calculation of the outputs corresponding to the generated input samples by using methods of classical dynamics and (iii) estimating statistics of the output process from sample outputs related to the previous step. For linear and non-linear systems driven by parametric impulsive inputs such as normal or non-normal white noises, a general integration method requires a considerable reduction of the integration step when the impulse occurs, treating the impuls…

Modal Analysis of Multi-Degrees-of-Freedom Systems with Singular Matrices: Analytical Dynamics Approach

Complex mechanical (e.g., multibody) systems with different types of constraints are generally performed through analytical dynamics methods. In some cases, however, it is possible that the (augmented) mass and/or stiffness matrices may derive to be singular; consequently, modal analysis, which is used extensively in the classical dynamics literature, fails. In this paper, if the uniqueness condition is satisfied by the constraints, a properly modified modal analysis is elucidated into analytical dynamics leading to the evaluation of the natural frequencies in a simple and straightforward way. Under that framework, advances of both classical and analytical dynamics are taken into considerat…

Complex Potential Function in Elasticity Theory: shear and torsion solution through line integrals

Aim of this paper is to introduce a basis formulation framed into complex analysis valid to solve shear and torsion problems. Solution, in terms of a complex function related to the complete tangential stress field, may be evaluated performing line integrals only. This basis formulation framed into elasticity problems may be a useful support for a boundary method to verify the accuracy of an approximation of function solution. The numerical applications stress the latter point and show the validity of these formulas since exact solutions may be reached for sections where the exact solution is known.

Analisi numerica degli effetti della deformazione di membrane a scambio ionico sulla distribuzione dei fluidi in canali di Elettrodialisi

L’elettrodialisi (ED) è una promettente tecnologia a membrana utilizzata in diversi campi, ad esempio nella dissalazione delle acque e nell’industria alimentare. L’ED usa un potenziale elettrico per indurre una migrazione selettiva di cationi ed anioni da una soluzione elettrolitica ad un’altra, sfruttando membrane a scambio ionico. Membrane anioniche e cationiche sono alternativamente collocate all’interno di una unità ED. A queste sono solitamente interposti spaziatori che prevengono il contatto tra le membrane e delineano i canali in cui scorrono le soluzioni. L’utilizzo di membrane profilate consente di costruire unità prive di tradizionali spaziatori a rete non conduttivi. In genere, l…

De Saint-Venant flexure-torsion problem handled by Line Element-less Method (LEM)

In this paper, the De Saint-Venant flexure-torsion problem is developed via a technique by means of a novel complex potential function analytic in all the domain whose real and imaginary parts are related to the shear stresses. The latter feature makes the complex analysis enforceable for the shear problem. Taking full advantage of the double-ended Laurent series involving harmonic polynomials, a novel element-free weak form procedure, labelled Line Element-less Method (LEM), is introduced, imposing that the square of the net flux across the border is minimized with respect to expansion coefficients. Numerical implementation of the LEM results in systems of linear algebraic equations involv…

On the Dynamics of Fractional Visco-Elastic Beams

With increasing advanced manufacturing process, visco-elastic materials are very attractive for mitigation of vibrations, provided that you may have advanced studies for capturing the realistic behavior of such materials. Experimental verification of the visco-elastic behavior is limited to some well-known low order models as the Maxwell or Kelvin models. However, both models are not sufficient to model the visco-elastic behavior of real materials, since only the Maxwell type can capture the relaxation tests and the Kelvin the creep tests, respectively. Very recently, it has been stressed that the most suitable model for capturing the visco-elastic behavior is the spring-pot, characterized …

Pressure-Induced Deformation of Pillar-Type Profiled Membranes and Its Effects on Flow and Mass Transfer

In electro-membrane processes, a pressure difference may arise between solutions flowing in alternate channels. This transmembrane pressure (TMP) causes a deformation of the membranes and of the fluid compartments. This, in turn, affects pressure losses and mass transfer rates with respect to undeformed conditions and may result in uneven flow rate and mass flux distributions. These phenomena were analyzed here for round pillar-type profiled membranes by integrated mechanical and fluid dynamics simulations. The analysis involved three steps: (1) A conservatively large value of TMP was imposed, and mechanical simulations were performed to identify the geometry with the minimum pillar density…

Random vibration of linear and nonlinear structural systems with singular matrices: A frequency domain approach

Abstract A frequency domain methodology is developed for stochastic response determination of multi-degree-of-freedom (MDOF) linear and nonlinear structural systems with singular matrices. This system modeling can arise when a greater than the minimum number of coordinates/DOFs is utilized, and can be advantageous, for instance, in cases of complex multibody systems where the explicit formulation of the equations of motion can be a nontrivial task. In such cases, the introduction of additional/redundant DOFs can facilitate the formulation of the equations of motion in a less labor intensive manner. Specifically, relying on the generalized matrix inverse theory, a Moore-Penrose (M-P) based f…

Performance-Based Engineering of Wind-Excited Structures: A General Methodology

The current prescriptive design philosophy that relies simply on meeting requirements stipulated in standards is shifting towards a performance-based design (PBD) approach for achieving designs that rationally meet society’s need for a truly safe built environment. Extensive research has facilitated the successful adoption of PBD in earthquake engineering, but the same cannot be said for wind engineering. Therefore, the need exists to initiate a similar effort by defining a framework that fully embraces the concepts of PBD during the design of building systems to resist severe wind events. This paper illustrates the development of such a PBD framework. In particular, a method is proposed sp…

A novel identification procedure from ambient vibration data for buildings of the cultural heritage

Ambient modal identification, also known as Operational Modal Analysis (OMA), aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., no initial excitation or known artificial excitation. This procedure for testing and/or monitoring historic buildings, is particularly attractive for civil engineers concerned with the safety of complex historic structures. However, since the external force is not recorded, the identification methods have to be more sophisticated and based on stochastic mechanics. In this context, this contribution will introduce an innovative ambient identification method based on appl…

Stochastic Response Of Fractionally Damped Beams

Abstract This paper aims at introducing the governing equation of motion of a continuous fractionally damped system under generic input loads, no matter the order of the fractional derivative. Moreover, particularizing the excitation as a random noise, the evaluation of the power spectral density performed in frequency domain highlights relevant features of such a system. Numerical results have been carried out considering a cantilever beam under stochastic loads. The influence of the fractional derivative order on the power spectral density response has been investigated, underscoring the damping effect in reducing the power spectral density amplitude for higher values of the fractional de…

OMA: From Research to Engineering Applications

Ambient vibration modal identification, also known as Operational Modal Analysis (OMA), aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., when there is no initial excitation or known artificial excitation. This method for testing and/or monitoring historical buildings and civil structures, is particularly attractive for civil engineers concerned with the safety of complex historical structures. However, in practice, not only records of external force are missing, but uncertainties are involved to a significant extent. Hence, stochastic mechanics approaches are needed in combination with the iden…

Linear ViscoElastic (LVE) Behaviour of Pure Bitumen via Fractional Model

AbstractBy fitting experimental data from static creep/recovery carried out on pure bitumen, it is shown that the fractional model proposed enables the description of both creep and recovery behaviour with fewer parameters than those needed by other models in the literature. In particular, the model is fitted to experimental data of complex modulus |G*| and phase angle δ° obtained from Dynamic Mechanical Analysis. Lastly, it is demonstrated that when the fractional model is used, complex modulus isotherms for a range of frequencies can be created simply starting from isochronals at f = 1Hz.

Hybrid Passive Control Strategies for Reducing the Displacements at the Base of Seismic Isolated Structures

In this paper, the use of hybrid passive control strategies to mitigate the seismic response of a base-isolated structure is examined. The control performance of three different types of devices used for reducing base displacements of isolated buildings is investigated. Specifically, the Tuned Mass Damper (TMD), the New Tuned Mass Damper (New TMD) and the Tuned Liquid Column Damper (TLCD), each one associated to a Base Isolated structure (BI), have been considered. The seismic induced vibration control of base-isolated structures equipped with the TMD, New TMD or the TLCD is examined and compared with that of the base-isolated system without devices, using real recorded seismic signals as e…

Fractional calculus application to visco-elastic solid

It is widely known that fractional derivative is the best mathematical tool to describe visco-elastic constitutive law. In this paper it is shown that as soon as we assume the creep compliance function as power law type, as in the linearized version of the Nutting equation, then the fractional constitutive law appears in a natural way. Moreover, using Nutting equation for the creep function, the relaxation modulus is also of power law type whose coefficients (intensity and exponent) are strictly related to those of the creep compliance. It follows that by a simple creep test (or relaxation test) by means of a best fitting procedure we may easily evaluate the parameters of Nutting equation a…

Stochastic analysis of external and parametric dynamical systems under sub-Gaussian Levy white-noise

In this study stochastic analysis of non-linear dynamical systems under α-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of α-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with α/2- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function …

Galerkin Scheme-Based Determination of Survival Probability of Oscillators With Fractional Derivative Elements

In this paper, an approximate semi-analytical approach is developed for determining the first-passage probability of randomly excited linear and lightly nonlinear oscillators endowed with fractional derivative elements. The amplitude of the system response is modeled as one-dimensional Markovian process by employing a combination of the stochastic averaging and the statistical linearization techniques. This leads to a backward Kolmogorov equation which governs the evolution of the survival probability of the oscillator. Next, an approximate solution of this equation is sought by resorting to a Galerkin scheme. Specifically, a convenient set of confluent hypergeometric functions, related to …

Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results

In capturing visco-elastic behavior, experimental tests play a fundamental rule, since they allow to build up theoretical constitutive laws very useful for simulating their own behavior. The main challenge is representing the visco-elastic materials through simple models, in order to spread their use. However, the wide used models for capturing both relaxation and creep tests are combinations of simple models as Maxwell and/or Kelvin, that depend on several parameters for fitting both creep and relaxation tests. This paper, following Nutting and Gemant idea of fitting experimental data through a power law function, aims at stressing the validity of fractional model. In fact, as soon as rela…

Time delay induced effects on control of linear systems under random excitation

Recursive formulas in terms of statistics of the response of linear systems with time delay under normal white noise input are developed. Two alternative methods are presented, in order to capture the time delay effects. The first is given in an approximate solution obtained by expanding the control force in a Taylor series. The second, available for the stationary solution (if it exists) gets the variance of the controlled system, with time delay in an analytical form. The efficacy loss in terms of statistics of the response is discussed in detail.

Deterministic and Random Vibration of Linear Systems with Singular Parameter Matrices and Fractional Derivative Terms

Both time- and frequency-domain solution techniques are developed for determining the response of linear multi-degree-of-freedom systems exhibiting singular parameter matrices and endowed with derivative terms of noninteger orders modeled as rational numbers. This is done based on the Moore-Penrose matrix inverse theory, in conjunction with a state variable formulation and with a complex modal analysis treatment. It is worth noting that, for the class of systems considered herein, this treatment also yields decoupled governing equations, thus facilitating further their numerical solution. Next, a generalization of the standard frequency-domain input-output (excitation-response) relationship…

Health monitoring of civil and aerospace structural components by guided ultrasonic waves

Combining TMD and TLCD: analytical and experimental studies

Abstract In these years several research efforts have been focused on developing efficient and reliable control devices for mitigating the structural response of tall and lightly damped buildings in case of strong dynamic excitations, such as wind and earthquake ones. In this context, Tuned Mass Dampers (TMDs) represent probably the most common control device due to their high control performances. On the other hand, Tuned Liquid Column Dampers (TLCDs) are increasingly becoming more popular because of some of their attractive features, cost-effectiveness among the others, even though they yield slightly less control performance compared to the classical TMDs. Aiming at combining the benefic…

Il Filtro Integrale Auto-Regressivo Continuo (I-ARC) per l’Analisi di Strutture Esposte al Vento

In questo studio viene proposto un metodo per la rappresentazione di processi aleatori Gaussiani e stazionari, utile a modellare la turbolenza della velocità del vento, introducendo la versione integrale del modello auto-regressivo discreto già proposto in precedenza. La rappresentazione di un processo aleatorio di assegnata funzione di correlazione viene condotta integrando un’equazione integro-differenziale in cui viene coinvolto un nucleo, che rappresenta la memoria del processo, in presenza di un rumore bianco Gaussiano. La soluzione dell’equazione rappresenta un campione del processo aleatorio della turbolenza della velocità del vento. E’ stato mostrato che il modello I-ARC fornisce, n…