Numerical modelling of thermoelastic processes using nonlinear theories with thermal relaxation time

D. V. Strunin, R. V. N. Melnik, A. J. Roberts


A nonlinear model of thermoelasticity is solved for a ring-shaped body with special attention given to the effect of relaxation time on the body dynamics. A spectral Galerkin method is used to accurately resolve spatial structures of temperature and displacement. A sequence of solutions is obtained for gradually increasing initial amplitude of the thermoelastic wave, showing a transition from a steady harmonic wave to singular solutions. Larger values of the relaxation time are shown to result in smoother temperature profiles. The dynamics generated by a localised heat release from an external source is studied. It is observed that the source excites a standing-like wave of the displacement while temperature monotonically decays.

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.