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Presentation of the general solution of three-dimensional dynamic equations of a transversely isotropic thermoelastic medium
B. D. Anninab, N. I. Ostrosablina a Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk, 630090, Russia
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.
Keywords:
transverse isotropy, thermoelasticity, thermal conductivity, Carrier–Gassmann condition, general solutions, plane waves.
Received: 26.11.2018 Revised: 26.11.2018 Accepted: 26.11.2018
Citation:
B. D. Annin, N. I. Ostrosablin, “Presentation of the general solution of three-dimensional dynamic equations of a transversely isotropic thermoelastic medium”, Prikl. Mekh. Tekh. Fiz., 60:2 (2019), 47–57; J. Appl. Mech. Tech. Phys., 60:2 (2019), 224–233
Linking options:
https://www.mathnet.ru/eng/pmtf458 https://www.mathnet.ru/eng/pmtf/v60/i2/p47
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