Search results for "Random vibration"
showing 10 items of 27 documents
Stochastic linearization of MDOF systems under parametric excitations
1992
Abstract The stochastic linearization approach is examined for non-linear systems subjected to parametric type excitations. It is shown that, for these systems too, stochastic linearization and Gaussian closure are two equivalent approaches if the former is applied to the coefficients of the Ito differential rule. A critical review of other stochastic linearization approaches is also presented and discussed by means of simple examples.
Numerical and experimental verification of a technique for locating a fatigue crack on beams vibrating under Gaussian excitation
2007
The stationary vibrations of a beam excited by Gaussian noise are strongly affected by the presence of a fatigue crack. Indeed, as soon as the crack arises the system response becomes non-linear due to crack breathing and a non-Gaussian behaviour is encountered. The paper presents both numerical and experimental investigations in order to assess the capability of the non-Gaussianity measures to detect crack presence and position. Monte Carlo method is applied to evaluate in time domain the higher order statistics of a cantilever beam modelled by finite elements. The skewness coefficient of the rotational degrees of freedom appears the most suitable quantity for identification purpose being …
Identification of stiffness, dissipation and input parameters of multi degree of freedom civil systems under unmeasured base excitations
2009
A time domain dynamic identification technique based on a statistical moment approach has been formulated for civil systems under base random excitations in the linear state. This technique is based on the use of classically damped models characterized by a mass proportional damping. By applying the Itô stochastic calculus, special algebraic equations that depend on the statistical moments of the response can be obtained. These equations can be used for the dynamic identification of the mechanical parameters that define the structural model, in the case of unmeasured input as well, and the identification of the input itself. Furthermore, the above equations demonstrate the possibility of id…
Stochastic response determination of structural systems modeled via dependent coordinates: a frequency domain treatment based on generalized modal an…
2019
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…
Deterministic and Random Vibration of Linear Systems with Singular Parameter Matrices and Fractional Derivative Terms
2021
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…
Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization
2003
This paper presents some properties of two restricted classes of multi-degree-of-freedom potential systems subjected to Gaussian white-noise excitations. Specifically, potential systems which exhibit damping terms with energy-dependent polynomial form are referred to. In this context, first systems with coupled stiffness terms and damping terms depending on the total energy are investigated. Then, systems with uncoupled stiffness terms and damping terms depending on the total energy in each degree-of-freedom are considered. For these two classes, it is found that algebraic relations among the stationary statistical moments of the energy functions can be derived by applying standard tools of…
On the derivation of the Fokker-Plank equation by using of Fractional calculus
2009
In this paper, fractional calculus has been used to find the spectral counterpart of the Fokker- Planck equations for non-linear systems driven by Lévy white noise processes. In particular it is shown that one can obtain the equation ruling the characteristic function of the response to a non-linear system, without using the Itô formula. Indeed, it is possible to reproduce the well-known results, already known in literature, by means of the characteristic function representation in terms of complex moments, recently proposed by the first two authors. The case of a-stable Lévy driven stochastic differential equation is also treated introducing an associated process constructed from the stabl…
Random vibration of linear and nonlinear structural systems with singular matrices: A frequency domain approach
2017
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…
Path integral solution by fractional calculus
2008
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.
Efficient solution of the first passage problem by Path Integration for normal and Poissonian white noise
2015
Abstract In this paper the first passage problem is examined for linear and nonlinear systems driven by Poissonian and normal white noise input. The problem is handled step-by-step accounting for the Markov properties of the response process and then by Chapman–Kolmogorov equation. The final formulation consists just of a sequence of matrix–vector multiplications giving the reliability density function at any time instant. Comparison with Monte Carlo simulation reveals the excellent accuracy of the proposed method.