Plane Waves in a Thermoelastic Solid

Abstract

In an isotropic, thermoelastic solid shear waves are unaltered by thermal effects. However, two distinct dilatational waves exist, both of which are dispersed and attenuated by the medium. One of the waves (denoted the E wave) is close in character to the pure elastic wave, the other wave (denoted the T wave) is similar in nature to the pure thermal wave. The properties of the two dilatational motions are studied and relations are given expressing the variation, in each, of phase velocity, amplitude attenuation, and specific loss with impressed frequency. For the E wave the result is verified that this disturbance propagates at the adiabatic velocity at low frequencies and at the isothermal velocity at very high frequencies. An explanation based on physical considerations is offered to account for this generally overlooked phenomenon. It is further found that the amplitude is attenuated exponentially as the square of the frequency at relatively low frequencies, but approaches finite value as the frequency increases without limit. The specific loss reaches maximum for the E wave, a minimum for the T wave, near the frequency whose period is equal to the relaxation time due to thermal currents. Finally, the ratios are computed of the amplitude of the temperature to the amplitude of the displacement in each of the two modes of motion. Numerical work indicates that, for metals at room temperature, the effect of coupling between elastic and thermal motions is very small.