The problem of the dynamics of a thermoelastic half-space under periodic surface forces and heat flows is solved using the model of coupled thermoelasticity. The Green’s tensor for one boundary value problem is constructed utilizing Fourier transformation. Analytical solutions for arbitrary surface forces and heat flow using the theory of generalized functions are constructed. To solve this boundary value problem, generalized function theory, tensor and differential algebra, the operator method, and integral transformations were used. The solutions obtained make it possible to investigate the thermal stress–strain state of an array with natural and artificial thermal sources and mass power forces acting at its surface.

使用耦合热弹性模型解决了周期性表面力和热流作用下热弹性半空间的动力学问题。利用傅立叶变换构造了一个边值问题的格林张量。利用广义函数理论构建了任意表面力和热流的解析解。为了解决该边值问题，使用了广义函数理论，张量和微分代数，算子方法以及积分变换。所获得的解决方案使得研究具有自然和人工热源以及作用在其表面的质量动力的阵列的热应力-应变状态成为可能。