Potential Method in the Linear Theories of Viscoelasticity and Thermoviscoelasticity for Kelvin-Voigt Materials

Abstract

In this paper the basic boundary value problems (BVPs) of steady vibrations in the linear theories of viscoelasticity and thermoviscoelasticity for Kelvin-Voigt materials are considered and some basic results of the classical theories of elasticity and thermoelasticity are generalized. The fundamental solutions of systems of equations of steady vibrations are constructed. The radiation conditions and basic properties of fundamental solutions are established. The properties of potentials of single-layer, double-layer and volume are given. The uniqueness theorems of the internal and external basic BVPs are established. Finally, the existence theorems for the internal and external basic BVPs are proved by means of the potential method and the theory of singular integral equations.