Unsteady dynamics of a sandwich plate under the influence of a cylindrical wave in an elastic medium

Abstract

The interaction of a sandwich plate with a damped cylindrical wave in the ground has been investigated. A sandwich plate is considered as a model of a barrier in the ground, described by a system of equations by V. N. Paimushin, placed in the ground dividing it into two parts. The plane problem formulation is considered. The boundary conditions correspond to the hinge attachment of the barrier, and the initial conditions are zero. A cylindrical damped wave is considered as an external influence. To describe the ground movement, the equations of the elasticity theory, the Cauchy relations and the physical principle, or equivalent displacements in potentials and the Lame equations are used. The problem is solved in a related formulation, where the movement of the plate and its surrounding media is considered together. All components of the equations of motion of the plate and media are decomposed into trigonometric series and the Laplace transform is applied to them. As the conditions for the contact of the plate and the ground, the equality of normal displacements at the boundary of the medium and the plate is assumed. It is also assumed that the pressure amplitudes and normal stresses coincide. After determining the constants from the contact conditions, the displacement values and the values of normal and tangential stresses are found, after which their originals are found.