Application of the method of discrete singularities to solve dynamic contact problems of the elasticity and hydrodynamics theory

Abstract

Two problems of continuum mechanics with mixed boundary conditions are considered: a dynamic antiplane problem for an elastic layer and the problem of oscillations of a plate on a layer of compressible fluid. The above problems are described by the Helmholtz equations for geometrically identical domains with the boundaries where the Dirichlet and Neumann conditions are interchanging. Boundary value problems are reduced to the boundary integral equations solved by the method of discrete singularities (sources and vortices). It is shown that the solutions of the above two problems have essentially different dynamic characteristics. To calculate proper frequencies of oscillations, asymptotical formulas have been obtained.