Steady-State Motion of a Line Mechanical/Heat Source Over a Half-Space: A Thermoelastodynamic Solution

An asymptotic solution within the bounds of steady-state coupled thermoelastodynamic theory is given for the surface displacement and temperature due to a line mechanical/heat source that moves at a constant velocity over the surface of a half-space. This problem is of basic interest in the fields of contact mechanics and tribology, and an exact formulation is considered. The results may serve as a Green’s function for more general thermoelastodynamic contact problems. The problem may also be viewed as a generalization of the classical Cole-Huth problem and the associated Georgiadis-Barber correction. Asymptotic expressions are obtained by means of the two-sided Laplace transform, and by performing the inversions exactly. The range of validity of these expressions is actually quite broad, because of the small value of the thermoelastic characteristic length appearing in the governing equations.