Uniqueness,variational,and reciprocity theorems in two-temperature Moore–Gibson–Thompson thermoelasticity

Abstract

This paper presents a study of thermoelasticity theory grounded in the recently developed two-temperature Moore–Gibson–Thompson (2TMGT) generalized thermoelasticity theory. We derive the fundamental governing equations for a homogeneous and isotropic medium within the context of 2TMGT. A primary objective is to establish key theoretical results, beginning with the uniqueness theorem for a mixed initial-boundary value problem in linear thermoelasticity under the current framework. Furthermore, we formulate a variational principle based on an appropriate functional corresponding to the governing equations of motion. This variational formulation offers deeper insights into the interactions between the mechanical and thermal aspects of the system. In addition, a reciprocity theorem is derived through the application of the Laplace transform method. The generalized results presented herein not only extend classical thermoelastic theorems but also enhance their applicability to a broader range of physical scenarios.