Dynamic Response of Non-uniformly Prestressed Thick Beam under Distributed Moving Load Travelling at Varying Velocity

Abstract

The dynamic response of non-uniformly prestressed thick beam under distributed moving load travelling at varying velocity is investigated in this paper. In order to obtain solution to the dynamical problem, a technique based on the method of Galerkin with the series representation of Heaviside function, was first used to transform the equation and thereafter the transformed equations were solved using Strubles asymptotic method and Laplace transformation techniques in conjunction with convolution theory.The displacement response for moving distributed force and moving distributed mass models for the dynamical problem are calculated for various time t and presented in plotted curves.Foremost, it is found that, the moving distributed force is not an upper bound for the accurate solution of the moving distributed mass problem, which shows that the inertia term must be considered for accurate assessment of the response to moving distributed load of elastic structural members . Analyses further shows that increase in the values of the structural parameters such as axial force N, shear modulus G and foundation stiffness K reduces the response amplitudes of non-uniformly prestressed thick beam under moving distributed loads. In order to verify the accuracy of the present method, the dynamic responses of a simply supported Timoshenko beam obtained by the present method and the frequency-domain spectral element method (SEM) are compared at two different velocities. The results shows that the dynamic responses obtained by the present method are almost identical to those obtained by using the SEM. Finally, for the same natural frequency, the critical speed for the beam transversed by moving distributed force is greater than that under the in uence of a moving distributed mass. Hence resonance is reached earlier in the moving distributed mass problem.