Numerical Modelling of Thermoelastic Processes Using Nonlinear Theories with Relaxation Time
Strunin, D.V., Melnik, R.V.N. and Roberts, A.J.
ANZIAM J. (Australian and New Zealand Industrial and Applied Mathematics Journal), 42E, 2000, C1356--C1378
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.