A coupled non-axisymmetric non-stationary problem of the thermoelasticity of a long cylinder

Inhomogeneous non-stationary heating of constructions of various purposes induces thermal strains and stresses that should be considered in the comprehensive analysis of elastic systems. The mathematical formulation of the considered linear threedimensional thermoelasticity problems includes coupled non-self-adjoint differential equations of motion and thermal conductivity. Due to their integration difficulty, axisym-metric problems are usually analyzed instead.
The purpose of this work is to develop a solution algorithm for the coupled non-axisymmetric non-stationary problem of the thermoelasticity of a long cylinder. On the internal surface of the hollow anisotropic cylinder, the temperature variation function is known; on the external surface, the convective heat transfer and environmental temperature are given. The rate of the temperature load does not affect the inertial characteristics of the cylinder. Therefore, the equilibrium and heat equations can be added to the initial system of linear equations.
The finite Fourier sine and cosine transforms and general biorthogonal transforms are used to study a non-self-adjoint system of differential equations and to develop a closed solution. The obtained solution allows one to determine the temperature field and the stress-strain state of a cylinder with its internal surface affected by non-stationary non-axisymmetric loading in terms of the temperature variation function.