Abstract
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.