An analytical-numerical solution to assess the dynamic response of viscoelastic plates to a moving mass

In this paper, the dynamics of a viscoelastic plate resting on a viscoelastic Winkler foundation and traversed by a moving mass is studied. The Laplace transform is employed to derive the governing equation of the problem. Thereafter, an analytical-numerical method is proposed in order to determine the dynamic response of the plate. The method is based on transforming the governing partial differential equation into a new solvable system of linear ordinary differential equations. To that extent, the proposed solution proves to be applicable to plates made of any viscoelastic material and with various boundary conditions. Moreover, the moving mass may travel at any arbitrary trajectory with no restriction. The capability of the method is demonstrated through several illustrative examples, wherein a comprehensive parametric study is performed to investigate the effect of various parameters on the response of the system. A comparison between the results obtained by the complete moving mass approach with those coming from the approximate solutions is also carried out. The comparative study suggests that neglecting the inertia of the moving mass in the problems where a relatively heavy mass is traveling at high speeds on a plate with a low level of viscosity leads, in general, to an unsafe design. Additionally, ignoring the effect of convective accelerations in the moving mass formulation results in an overly uneconomical design in most cases. However, for large values of viscosity, the accuracy of the approximate methods further improves, and those methods can be used to reasonably estimate the response. (C) 2017 Published by Elsevier Inc.