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The response of a Timoshenko beam with uniform cross-section and infinite length supported by a generalized Pasternak-type viscoelastic foundation subjected to an arbitrary-distributed harmonic moving load is studied in this paper. Governing equations are solved using complex Fourier transformation in conjunction with the residue and convolution integral theorems. The solution is directed to compute the deflection, bending moment and shear force distribution along the beam length. A parametric study is carried out for an elliptical load distribution and influences of the load speed and frequency on the beam responses are investigated. © 2004 Elsevier Ltd. All rights reserved  

Application of curved beams in special structures requires a special analysis. In this study, the differential quadrature method (DQM) as a well-known numerical method is utilized in the dynamic analysis of the Euler-Bernoulli curved beam problem with a uniform cross section under a constant moving load. DQ approximation of the required partial derivatives is given by a weighted linear sum of the function values at all grid points. A prismatic semicircular arch with simply supported boundary conditions is assumed. The accuracy of the obtained results is corroborated by employing the Galerkin and finite element methods. Finally, the convergence rate of the DQM and Finite Element Method (FEM)... 

The response of an infinite Timoshenko beam subjected to a harmonic moving load based on the thirdorder shear deformation theory (TSDT) is studied. The beam is made of laminated composite, and located on a Pasternak viscoelastic foundation. By using the principle of total minimum potential energy, the governing partial differential equations of motion are obtained. The solution is directed to compute the deflection and bending moment distribution along the length of the beam. Also, the effects of two types of composite materials, stiffness and shear layer viscosity coefficients of foundation, velocity and frequency of the moving load over the beam response are studied. In order to... 

The dynamics of nonlinear thin plates under influence of relatively heavy moving masses is considered. By expansion of the solution as a series of mode functions, the governing equations of motion are reduced to an ordinary differential equation for time development of vibration amplitude, which is Duffing's oscillator with time varying coefficients. Through the application of Banach's fixed-point theorem, the periodic solutions are predicted. The method presented in this paper is general so that the response of plate to moving force systems can also be considered. © 2002 Published by Elsevier Science Ltd  

This paper presents the linear dynamic response of uniform beams with different boundary conditions excited by a moving load, based on the Elder-Bernouli beam theory. Using a dynamic green function, effects of different boundary conditions, velocity of load and other parameters are. assessed and some of the numerical results are compared with those given in the. references. © Sharif University of Technology, June 2009  

Forced vibration of a porous functionally graded (FG) cylindrical microshell due to a moving point load with constant velocity is studied for the first time. Through the thickness of microshell, there are even-type or uneven-type porosities. Therefore, material properties of the microshell become porosity-dependent and are described via modified power-law function. For micro-scale shells, small size effects due to non-uniform strain field can be considered via strain gradient theory (SGT). At first, the governing equations of the microshell are converted to new equations in Laplace domain. Then, time response of the microshell will be obtained implementing inverse Laplace transform... 

One of the engineers concern in designing bridges and structures under moving load is the uniformity of stress distribution. In this paper the analysis of a variable cross-section beam subjected to a moving concentrated force and mass is investigated. Finite element method with cubic Hermitian interpolation functions is used to model the structure based on Euler-Bernoulli beam and Wilson-⊖ direct integration method is implemented to solve time dependent equations. Effects of cross-section area variation, boundary conditions, and moving mass inertia on the deflection, natural frequencies and longitudinal stresses of beam are investigated. Results indicates using a beam of parabolically... 

The response of infinite beams supported by nonlinear viscoelastic foundations subjected to harmonic moving loads is studied. A straightforward solution technique applicable in the frequency domain is presented in this paper. The governing equations are solved using a perturbation method in conjunction with complex Fourier transformation. A closed-formed solution is presented in an integral form based on the presented Green's function and the theorem of residues is used for the calculation of integrals. The solution is directed to compute the deflection and bending moment distribution along the length of the beam. A parametric study is carried out and influences of the load speed and... 

This paper presents the dynamic response of uniform Timoshenko beams with arbitrary boundary conditions using Dynamic Green Function. An exact and direct modeling technique is stated to model beam structures with arbitrary boundary conditions subjected to the external load that is an arbitrary function of time t and coordinate x and the concentrated moving load. This technique is based on the Dynamic Green Function. The effect of different boundary conditions, load, and other parameters is assessed. Finally, some numerical examples are shown to illustrate the efficiency and simplicity of the new formulation based on the Dynamic Green Function  

A composite beam with single delamination under the action of moving load has been modeled accounting for the Poisson's effect, shear deformation, and rotary inertia. The existence of the delamination changes the stiffness of the structure, and this affects the dynamic response of the structure. We have used a constrained mode to simulate the behavior between the delaminated surfaces. Based on this mode, eigensolution technique is used to obtain the natural frequencies and their corresponding mode shapes for the delaminated beam. Then, the Ritz method is adopted to derive the dynamic response of the beam subjected to a moving load. The obtained results for the free and forced vibrations of... 

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... 

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 are derived using Hamilton's principle. A moving mass traveling on an arbitrary trajectory acts as an external excitation for the system. The effect of moving mass inertia is considered using all the out-of-plane translational acceleration components. The method of eigenfunction expansion is used to decouple 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 by determining the... 

The vibration response of a Timoshenko beam supported by a viscoelastic foundation with randomly distributed parameters along the beam length and jected to a harmonic moving load, is studied. By means of the first-order two-dimensional regular perturbation method and employing appropriate Green's functions, the dynamic response of the beam consisting of the mean and variance of the deflection and of the bending moment are obtained analytically in integral forms. Results of a field measurement for a test track are utilized to model the uncertainty of the foundation parameters. A frequency analysis is carried out and the effect of the load speed on the response is studied. It is found that the... 

Dynamic response of infinite beams supported by random viscoelastic Pasternak foundation subjected to harmonic moving loads is studied. Vertical stiffness in the support is assumed to follow a stochastic homogeneous field consisting of a small random variation around a deterministic mean value. By employing the first order perturbation theory and calculating appropriate Green's functions, the variance of the deflection and bending moment are obtained analytically in integral forms. To simulate the induced uncertainty, two practical cases of cosine and exponential covariance are utilized. A frequency analysis is performed and influences of the correlation length of the stiffness variation on... 

Forced and free vibrational analyses of viscoelastic nanotubes containing fluid under a moving load in complex environments incorporating surface effects are conducted based on the nonlocal strain gradient theory and the Rayleigh beam model. To model the internal nanoflow, the slip boundary condition is employed. Adopting the Galerkin discretization approach, the reduced-order dynamic model of the system is acquired. Analytical and numerical methods are exploited to determine the dynamic response of the system. The impacts of geometry, scale parameter ratio, Knudsen number, fluid velocity, rotary inertia parameter, viscoelastic parameter, surface residual stress, surface elastic modulus, and... 

The governing differential equation of motion of a thin rectangular plate excited by a moving mass is considered. The moving mass is traversing on the plate's surface at arbitrary trajectories. Eigenfunction expansion method is employed to solve the constitutive equation of motion for various boundary conditions. Approximate and exact expressions of the inertial effects are adopted for the problem formulation. In the approximate formulation, only the vertical acceleration component of the moving mass is considered while in the exact formulation all the convective acceleration components are included in the problem formulation as well. Parametric studies are carried out to investigate the... 

In this paper, nonlinear dynamical behavior of a rectangular plate traveled by a moving mass as well as an equivalent concentrated force with non-constant velocity is studied. The nonlinear governing coupled partial differential equations (PDEs) of motion are derived by energy method using Hamilton's principle based on the large deflection theory in conjuncture with the von-Karman strain-displacement relations. Then Galerkin's method is used to transform the equations of motion into a set of three coupled nonlinear ordinary differential equations (ODEs) which then is solved in a semi-analytical way to get the dynamical response of the plate. Also, by using the Finite Element Method (FEM)...