ABSTRACTAn analytical solution for the generalized displacement–temperature equations of motion and energy equation is introduced in terms of three scalar potential functions for a thermoelastic isotropic material. The generalized equations are considered within the context of Lord and Shulman theory (L.S. Theory). The potential functions are governed by a wave or a repeated wave–heat equation. The completeness of the solution is proved based on a retarded Newtonian potential function, the perturbation theory, and the solutions of the repeated wave equation and heat equation. The complete solution for the coupled displacement–temperature equations of motions and energy equation is deduced as a special case. The degenerated case to elastodynamics is obtained.

中文翻译：

---

基于Lord-Shulman理论求解广义热弹性问题的一组势函数的完备性

摘要根据热弹性各向同性材料的三个标量势函数，引入了广义位移-温度运动方程和能量方程的解析解。广义方程是在 Lord 和 Shulman 理论（LS 理论）的背景下考虑的。势函数由波或重复的波热方程控制。基于延迟牛顿势函数、微扰理论以及重复波动方程和热方程的解，证明了解的完备性。运动和能量方程的耦合位移-温度方程的完全解作为特例推导出来。得到了弹性动力学的退化情况。