Unsteady elastic diffusion torsional vibrations of a rectangular Kirchhoff-Love plate

Abstract

We investigated unsteady elastic diffusion torsional vibrations of a simply supported rectangular isotropic Kirchhoff-Love plate. The problem solution is sought in integral form, and Green's functions are kernels of these integrals. We used the Laplace transform in time and the expansion into double trigonometric Fourier series in spatial coordinates to find the Green's functions. The Green's functions in the image domain are represented as rational functions depending on the Laplace transform parameter. The transition to the original domain is done analytically through residues and tables of operational calculus. Analytical expressions of the Green's functions are obtained. A study of unsteady mechanical and diffusion fields interaction is done for an isotropic plate using a three-component continuum.