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Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatial domain using generalized moving least square method (GMLSM) and then, discrete equations of motion based on Lagrange's equation are obtained. Maximum deflection and bending moments are considered as the important design parameters. The design parameter spectra in terms of mass weight and velocity of the moving mass are presented for multispan viscoelastic beams as well as various values of relaxation rate and beam span number. A reasonable good agreement is achieved between... 

Dynamic deformations of beams and plates under moving objects have extensively been studied in the past. In this work, the dynamic response of geometrically nonlinear rectangular elastic plates subjected to moving mass loading is numerically investigated. A rectangular von Karman plate with various boundary conditions is modeled using specifically developed geometrically nonlinear plate elements. In the available finite element (FE) codes the only way to distinguish between moving masses from moving loads is to model the moving mass as a separate entity. However, these procedures still do not guarantee the inclusion of all inertial effects associated with the moving mass. In a prepared... 

In this paper, a comprehensive assessment of design parameters for various beam theories subjected to a moving mass is investigated under different boundary conditions. The design parameters are adopted as the maximum dynamic deflection and bending moment of the beam. To this end, discrete equations of motion for classical Euler-Bernoulli, Timoshenko and higher-order beams under a moving mass are derived based on Hamilton's principle. The reproducing kernel particle method (RKPM) and extended Newmark-β method are utilized for spatial and time discretization of the problem, correspondingly. The design parameter spectra in terms of the beam slenderness, mass weight and velocity of the moving... 

This paper presents a numerical parametric study on design parameters of multispan viscoelastic shear deformable beams subjected to a moving mass via generalized moving least squares method (GMLSM). For utilizing Lagrange's equations, the unknown parameters of the problem are stated in terms of GMLSM shape functions and the generalized Newmark-β scheme is applied for solving the discrete equations of motion in time domain. The effects of moving mass weight and velocity, material relaxation rate, slenderness, and span number of the beam on the design parameters and possibility of mass separation from the base beam are scrutinized in some detail. The results reveal that for low values of beam... 

The governing differential equation of motion for an undamped thin rectangular plate with a number of bonded piezoelectric patches on its surface and arbitrary boundary conditions is derived using Hamilton's principle. A moving mass traveling on an arbitrary trajectory acts as an external excitation for the system. The effect of the moving mass inertia is considered using all the out-of-plane translational acceleration components. The method of eigenfunction expansion is used to transform the equation of motion into a number of coupled ordinary differential equations. A classical closed-loop optimal control algorithm is employed to suppress the dynamic response of the system, determining the... 

Abstract In this study, the response spectrum of a time-varying system such as a beam subjected to moving masses under a harmonic and earthquake support excitations is explored. The excitations are supposed to act on the horizontal directions of the beam axis. The inertial effect of the moving masses on the natural frequencies of the beam for different cases of loading is investigated and a critical value of a so called parameter "mass staying time" is presented to avoid dynamic instability of the system. Finally, some 3D response spectra for different supports excitations as well as the beam natural frequencies are depicted  

In this article, OPSEM (Orthonormal Polynomial Series Expansion Method) is developed as a new computational approach for the evaluation of thin beams of variable thickness transverse vibration. Capability of the OPSEM in assessing the free vibration frequencies and mode shapes of an Euler-Bernoulli beam with varying thickness is discussed. Multispan continuous beams with various classical boundary conditions are included. Contribution of BOPs (Basic Orthonormal Polynomials) in capturing the beam vibrations is also illustrated in numerical examples to give a quantitative measure of convergence rate. Furthermore, OPSEM is adopted for the forced vibration of a thin beam caused by a moving mass....