Non-stationary vibrations of a plate on an elastic half-space

Abstract

The problem of non-stationary vibrations of an infinite elastic plate of constant thickness resting on an elastic isotropic half-space is solved. The equations of the plate motion take the rotary inertia and transverse shear deformations into account. Both welded and smooth contact between layer and half-space are considered. Non-stationary vibrations are excited by snap-action loads on the plate, resulting in two types of plane surfaces of strong discontinuities propagating in the half-space. The solution behind the wavefronts up to the contact boundary is constructed by using ray series. Unknown functions entering into the ray series coefficients and into the equations of the plate motion are determined from the boundary conditions of the contact interaction between the plate and the half-space. The time-dependencies of the plate displacements, angle of rotation and contact stresses are obtained. The Uflyand-Mindlin plate deflections are compared with those of a classical plate for both welded and smooth contact.