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…
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, …
Moving multi-loads problem in layered cracked beams with interlayer slip
This contribution concerns the vibration response of layered cracked uniform beams with interlayer slip under moving multiple loads. Considering a linear constitutive relation between the horizontal slip and the interlaminar shear force, the Euler-Bernoulli hypothesis is assumed to hold for each layer separately. Modeling cracks as internal elastic rotational joints, related discontinuities of the response variables are treated by the theory of generalized functions. In this manner, exact eigenfunctions are derived from a characteristic equation built as determinant of 6x6 matrix, for any number of cracks. Building pertinent orthogonality conditions for the deflection eigenfunctions, the re…
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…
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 …
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…
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…
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…
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…
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…
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…