External problems of steady vibrations in the theory of elastic materials with a triple porosity structure

Abstract

In this paper, the linear theory of elasticity for materials with a triple porosity (macro, meso and micro levels of porosities) structure based on the volume fraction concept is considered. The external boundary value problems (BVPs) of steady vibrations of this theory are investigated. Namely, the uniqueness theorem for classical solutions of these BVPs is established. Then, the basic properties of the surface (single‐layer and double‐layer) potentials are given. Finally, on the basis of the properties of potentials, the existence theorems for classical solutions of the above mentioned BVPs of steady vibrations are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.