Elastic waves induced by surface heating in a half-space

Rapid surface heating will induce waves in an elastic material. Closed-form solutions for the resulting longitudinal and transverse thermal stresses are derived using Laplace Tran forms. The model is one-dimensional, consisting of a half-space subjected to a step change in the surface heating. The transverse stress at the wave peak is found to exceed the surface stress for short times, while for long times the surface stress far exceeds either of the stresses at the wave peak. Both the longitudinal and transverse stresses at the peak of the wave reach steady-state values after a few dimensionless times.