Presentation of the General Solution of Three-Dimensional Dynamic Equations of a Transversely Isotropic Thermoelastic Medium
B. D. Annin1,2, N. I. Ostrosablin1
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk State University, Novosibirsk, 630090, Russia
Keywords: трансверсальная изотропия, термоупругость, теплопроводность, условие Карриера - Гассмана, общие решения, плоские волны, transverse isotropy, thermoelasticity, thermal conductivity, Carrier-Gassmann condition, general solutions, plane waves
Abstract
A presentation of the general solution of the equations of dynamics of a transversely isotropic thermoelastic medium is obtained in the case where the Carrier-Gassmann condition is satisfied with due allowance for the additional expression relating the temperature stress coefficients to the elasticity moduli. The displacements are expressed via three resolving potentials satisfying three inhomogeneous quasi-wave equations. The potentials are related by the heat conduction equation. A presentation of the solution with the use of the stress and displacement functions is provided. Two displacement functions are determined by solving the system of two homogeneous equations, which do not involve the temperature. After these displacement functions are determined, the temperature can be found from the third equation. The resultant presentation of the solution also yields the solution of the static equations of thermoelasticity.
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