Static and Dynamic Analyses of Rectangular Plates with Stepped Thickness Subjected to Moving Loads

Abstract

This chapter presents the analytical methodology for the dynamic problems of an isotropic rectangular plate with arbitrarily and eccentrically stepped thickness in bending state, subjected to moving loads along with the effect of additional mass. The discontinuous variation in the rigidity and mass of the plates due to the voids is also expressed as a continuous function by means of the extended Dirac function. First, the general governing equations for rectangular plates with stepped thickness is proposed on the basis of the Kirchhoff-Love hypothesis. Second, the analytical methodologies for the dynamic problems are presented by means of the Galerkin method. Third, for practical use, the approximate solutions for the dynamic problems are proposed in closed-form solution.