Three-Dimensional Dynamic Problem of the Theory of Elasticity for a Parallelepiped

Abstract

We study a three-dimensional problem of the theory of elasticity for a rectangular parallelepiped in the case of steady-state forced vibrations. By the method of superposition, we reduce the problem to an infinite system of linear algebraic equations for the coefficients of double Fourier series. For this infinite system, we prove that the conditions of quasiregularity are satisfied and that the bounded solution exists. We also construct the asymptotics that describes the behavior of unknowns in the infinite system. The method is illustrated by several numerical examples.