Interaction of a Spherical Wave with a Rectangular Plate in a Ground.
- In Recent Developments in the Theory of Shells. Springer, Cham., p.443-457, 2019 .
The vibration-absorbing properties of the plate under the action of a spherical harmonic wave propagating in the ground are studied. An elastic isotropic medium is used as a ground model. The main aim of this study is to determine the total vector field of accelerations. The mathematical formulation of the problem includes the assignment of the ingoing wave, the dynamic equations of the ground and the plate, the boundary conditions for the obstacle and the medium, the conditions at infinity for medium, and the conditions of contact of the medium with the obstacle, where we neglect the connection of the plate to the ground. The dynamic equations of the plate is described by the system of equations of V.N. Paimushin. The kinematic parameters of the plate and the parameters of the disturbed stress-strain state of the medium are represented in the form of double trigonometric series satisfying the boundary conditions. After that, the constants of integration, displacement, and vibration acceleration are determined.