Steady-State Response of a Thermoelastic Half-Space to the Rapid Motion of Surface Thermal/Mechanical Loads

Shear and normal tractions and a heat flux are applied to a largely arbitrary area that moves with constant subsonic speed over a half-space surface. The half-space is a coupled thermoelastic solid of the Jeffreys type, so that the governing steady-state equations involve three thermoelastic characteristic lengths and a dimensionless coupling constant. This constant and one of the lengths remain in the limit as the solid reduces to the standard coupled thermoelastic material. The problem is solved exactly in an integral transform space, and asymptotic expressions for the normal displacement and the temperature change induced on the half-space surface are extracted. These are in principle valid for large distances from the loading zone as measured along its line of travel but, because the scaling dimension is of O(10^-14)μ m, they are robust. Exact inversions are performed, and the results show marked dependence on both loading zone speed and thermoelastic parameters. Indeed, the role of the latter is enhanced as the speed is increased. Singular behavior is found, in particular, when the loading zone moves with the effective thermoelastic Rayleigh speed, an exact formula for which is also given. This revised version was published online in August 2006 with corrections to the Cover Date.