Modeling of elastic-diffusion vibrations of a hinged Timoshenko plate under the action of a distributed surface load

We consider the unsteady problem of a homogeneous orthotropic hinged Timoshenko elastic-diffusion plate under the action of a mechanical distributed surface load bending. The initial mathematical formulation of the problem includes the system of elastic diffusion equations for a continuum, which takes into account the finite diffusion perturbations propagation velocity. The equations of unsteady elastic-diffusion vibrations of the plate are obtained from the equations for a continuum using the generalized principle of virtual displacements and hypotheses of Timoshenko theory. The solution is sought using Laplace transform and expansion into Fourier series. The originals are found analytically, using residues and tables of operational calculus.