Steady Vibration Problems in the Theory of Moore–Gibson–Thompson Thermoelasticity for Materials With Voids

ABSTRACT In this paper, the linear theory of Moore–Gibson–Thompson (MGT) thermoelasticity for materials with voids is examined, taking into account the coupled effect of material deformation, the concept of pore volume fraction, and the MGT law of heat conduction. The basic boundary value problems (BVPs) associated with steady vibrations within this framework are investigated. Specifically, the integral representations of regular vector functions are obtained, the surface (single‐layer and double‐layer) and volume potentials are constructed, and their essential properties are established. These BVPs are reduced to singular integral equations, which are always solvable and for which Noether's theorems hold. Finally, the existence theorems for classical solutions to the internal and external BVPs are proven using the potential method and the theory of singular integral equations.