Rectangular Isotropic Kirchhoff-Love Plate on an Elastic Foundation under the Action of Unsteady Elastic Diffusion Perturbations

Abstract

We study unsteady elastic diffusion vibrations of a freely supported rectangular isotropic Kirchhoff-Love plate on an elastic foundation, which is under the action of a distributed transverse load. A model that describes coupled elastic diffusion processes in multicomponent continuum is used for the mathematical problem formulation. The longitudinal and transverse vibrations equations of a rectangular isotropic Kirchhoff-Love plate with diffusion were obtained from the model using the d'Alembert variational principle. The problem solution of unsteady elastic diffusion plate vibrations is sought in integral form. The bulk Green's functions are the kernels of the integral representations. To find the Green's functions, we used the Laplace transform in time and the expansion into double trigonometric Fourier series in spatial coordinates. Green's functions in the image domain are represented in the form of rational functions depends on the Laplace transform parameter. The transition to the original domain is done analytically through residues and tables of operational calculus. The bulk Green's functions analytical expressions are obtained. Using a two-component continuum, a numerical study of unsteady mechanical and diffusion fields interaction is done for an isotropic plate. The solution is presented in analytical form, as well as in the form of three-dimensional graphs of the displacement fields and concentration increments on time and coordinates.

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