Thermoelastic wave propagation in a rotating elastic mediumwithout energy dissipation

Abstract

A study is made of the propagation of time‐harmonic plane thermoelastic waves of assigned frequency in an infinite rotating medium using Green‐Naghdi model (1993) of linear thermoelasticity without energy dissipation. A more general dispersion equation is derived to examine the effect of rotation on the phase velocity of the modified coupled thermal dilatational shear waves. It is observed that in thermoelasticity theory of type II (Green‐Naghdi model), the modified coupled dilatational thermal waves propagate unattenuated in contrast to the classical thermoelasticity theory, where the thermoelastic waves undergo attenuation (Parkus, Chadwick, and Sneddon). The solutions of the more general dispersion equation are obtained for small thermoelastic coupling by perturbation technique. Cases of high and low frequencies are also analyzed. The rotation of the medium affects both quasielastic dilatational and shear wave speeds to the first order in ω for low frequency, while the quasithermal wave speed is affected by rotation up to the second power in ω. However, for large frequency, rotation influences both the quasidilatational and shear wave speeds to first order in ω and the quasithermal wave speed to the second order in 1/ω.