Thermoelastic plane waves without energy dissipation in a half-space due to time-dependent heating of the boundary

The linear theory of thermoelasticity without energy dissipation for homogeneous and isotropic materials is used to study plane waves in a half-space. The waves are supposed to be caused by a time-dependent heating of the stressfree boundary, which includes (i) sudden heating to a constant temperature, (ii) smooth heating for all times, (iii) smooth heating followed by sudden cooling, and (iv) smooth heating that becomes constant after a lapse of time, among its particular cases. The Laplace transform method is used to solve the problem. Exact solutions, in closed form, for the displacement, temperature, and stress fields are obtained and analyzed. Numerical results that illustrate the theoretical analysis are presented.