Modelling of rectangular Kirchhoff plate oscillations under unsteady elastodiffusive perturbations

Abstract

We study unsteady elastic-diffusion vibrations of a rectangular isotropic Kirchhoff plate. The coupled elastic-diffusion multicomponent continuum model is used to formulate the problem. We are using the d’Alembert variational principle to obtain from the model the equations of longitudinal and transverse vibrations of a rectangular isotropic elastodiffusive Kirchhoff plate. The problem solution is sought in integral form. The kernels of integral representations are the Green’s functions. For their determination, the Laplace transform and expansion in double Fourier series are used. As an example, we consider the bending of a simply supported plate. The effect of bending on the diffusion processes in the plate is investigated.