On the Solutions of Equations of the Linear Thermoviscoelasticity Theory for Kelvin–Voigt Materials with Voids

Abstract

In this article, the linear theory of thermoviscoelasticity for Kelvin–Voigt materials with voids is considered. The fundamental solution of the system of equations of steady vibrations is constructed by means of elementary functions and its basic properties are established. The representation of a Galerkin-type solution is obtained. The formula of representation of the general solution for the system of homogeneous equations of steady vibrations in terms of six metaharmonic functions is established. The completeness of these representations of solutions is proved.

Keywords:

• Galerkin-type solution
• Kelvin–Voigt materials with voids
• Representation of solution
• Steady vibrations
• Thermoviscoelasticity

ACKNOWLEDGMENT

The author is grateful to the reviewer for useful comments and fruitful suggestions.