ONE-DIMENSIONAL GREEN'S FUNCTION IN TEMPERATURE-RATE DEPENDENT THERMOELASTICITY

Abstract

This article presents a study of the one-dimensional thermoelastic wave produced by an instantaneous plane source of heat in an infinite body of the G-L type. The wave can be expressed by the power series of Neumann's type associated with two wave-like operators of the G-L theory; and the series are uniformly convergent on the whole space-time domain except for the two plane wave fronts parallel to the plane of heat source, and for a large range of constitutive variables. Moreover, a restriction of the wave to a semispace lying to the right of the heat source plane represents a thermoelastic response of the semispace to short laser pulse when the boundary of semispace is clamped and the laser generates a heat on the boundary only; the response is shown to be a sum of two plane waves propagating from the boundary into the semispace depth with two different velocities v_i and two different attenuations h_i, (i = 1, 2) in such a way that damping of the faster wave is smaller than that of the slower one (i.e., v2 > v, > 0 and ht > h2 > 0); and on each of the wave fronts the displacement suffers a finite jump while the heat flux behaves like a Dirac delta pulse. Numerical analysis of the wave indicates that the displacement field (finite part of the heat flux field) in a fixed cross section of the semispace is dominated by that part of the displacement (finite part of the heat flux) which is connected with the faster wave passing through the cross section.