Abstract
The present paper deals with thermoelastic problems of finitely long hollow cylinder com-posed of two different materials with axial sym- metry. The medium is traction-free, with neglig-ible body forces and with internal and external heat generations. The governing equations for different theories of the generalized thermoe-lasticity are written in terms of displacement and temperature increment. The exact solution of the problem; using different theories of generalized thermoelasticity; has been deduced. The analytical expressions for displacements, temperature and stresses are found in final forms, and a numerical example has been taken to discuss the effect of the relaxation times. Finally, the results have been illustrated graphi- cally to find the responses of different theories.
Highlights
The governing equations for displacement and temperature fields in the linear dynamical theory of classical thermoelasticity consist of the coupled partial differential equation of motion and Fourier’s law of heat conduction equation
This amounts to the remark that the classical thermoelasticity predicts a finite speed for predominantly elastic disturbances but an infinite speed for predominantly thermal disturbances, which are coupled together
Biot [1] formulated the theory of coupled thermoelasticity to eliminate the paradox inherent in the classical uncoupled theory of thermoelasticity that the elastic changes have no effect on the temperature
Summary
The governing equations for displacement and temperature fields in the linear dynamical theory of classical thermoelasticity consist of the coupled partial differential equation of motion and Fourier’s law of heat conduction equation. The equation for displacement field is controlled by a wave type hyperbolic equation, whereas that for the temperature field is a parabolic diffusion type equation This amounts to the remark that the classical thermoelasticity predicts a finite speed for predominantly elastic disturbances but an infinite speed for predominantly thermal disturbances, which are coupled together. Yang and Chen [10] discussed the transient response of one-dimensional quasi-static coupled thermoelasticity problems of an infinitely long annular cylinder composed of two different materials. Lee [11] solved the two-dimensional, quasi-static coupled, thermoelastic problem of finitely long hollow cylinder composed of two different materials with axial symmetry. Zenkour et al [15] presented the static bending response for a supported functionally graded rectangular plate subjected to a through-thethickness temperature field under the effect of various theories of generalized thermoelasticity with relaxation times. The results have been illustrated graphically to find the differences between the different generalized theories of thermoelasticity
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