Dynamic thermoelasticity problem for a finite hollow cylinder with a cut along the generatrix

Abstract

We consider the steady state problem of incoherent thermoelasticity for a finite hollow elastic cylinder on the inner and outer cylindrical surfaces of which ideal contact conditions are given. Without limiting the generality of reasoning, we consider a dynamic normal load applying at the upper face of the cylinder, and there are no tangential stress there. The bottom face of the cylinder is fixed. It is required to determine the thermos-wave field of the cylinder under steady state oscillations.To solve this problem, it is proposed to reduce the equations of dynamic incoherent thermoelasticity relatively to the displacements to two jointly and one separately solved equations. The solution of the two separately solved problems is carried out by the method of integral transformations, which allows us to construct the exact solutions for the separately solved problems in the explicit forms. In the case of the problem formulated using a system of two partial differential equations, it is proposed to use the apparatus of a matrix differential calculus. The matrix Greens function is constructed and the solution of the problem is derived in explicit form.