Modeling of unsteady elastic diffusion transverse vibrations of the isotropic simply supported Timoshenko plate


The unsteady problem of a homogeneous isotropic Timoshenko plate bending taken into account diffusion is considered. The initial mathematical formulation includes a system of equations of rectangular isotropic plate unsteady vibrations, obtained from a general model of elastic diffusion for continuum using the d'Alembert variational principle. An initial-boundary value problem is formulated, and Green's functions are found in the problem of a simply supported Timoshenko plate bending. In the example of a three-component rectangular plate under the action of a pair of bending moments, the interaction effects of mechanical and diffusion fields and the influence of relaxation processes on the kinetics of mass transfer are modelled. The calculation results are presented in analytical and graphical forms.