Magneto-thermo-elastic plane waves in rotating media

Abstract

A study is made of the propagation of plane harmonic waves in an infinite conducting thermo-elastic solid permeated by a primary uniform magnetic field when the entire elastic medium is rotating with a uniform angular velocity. A more general dispersion relation is obtained to determine the effects of rotation, relaxation time and the external magnetic field on the phase velocity of the waves. This result indicates that if the primary magnetic field has a transverse component, then the longitudinal and transverse components of the displacement field are linked together. For the case of low frequency ( Gc ⪡ 1 where κ is the ratio of the wave frequency to the characteristic frequency), the rotation and the thermal relaxation time are found to have no influence on the phase velocity, and the attenuation factor for both finite and infinite electrical conductivity. In the case of high frequency ( κ ⪢ 1), no effect of rotation on the phase speed is observed to the first order of ( 1 κ ), while the relaxation time affects both the phase velocity and the specific energy loss. However, the effects of rotation on the phase speed, the attenuation factor, and the specific energy loss are found only to the second order of ( 1 κ ) in the case of high frequency. Several limiting cases of interest are discussed.