Analytical Solution of Dynamic Analysis of Shear Flexible Clamped Rectangular Plates

A study on the suitability of a set of solution functions in an analytical solution approach for the dynamic response of a clamped, moderately-thick plate subjected to a dynamic load is presented. The solution methodology involves obtaining free vibration responses using a recently developed analytical solution approach based on the double Fourier series equations proposed by Kabir and Chaudhuri, and applying the modal superposition method in solving the dynamic response. The equilibrium equations for the plate are defined by a set of three highly-coupled partial differential equations that are based on the Mindlin theory. The solution functions are assumed in the form of double Fourier series that satisfy the boundary conditions. The dynamic load considered is a step impulse load applied at the center of the plate. Results include convergence characteristics of transverse displacement and moment and variation of these quantities with respect to aspect ratios. These analytical solutions are useful for testing the accuracy of numerical methods.