Propagation of waves in random rotating infinite magneto-thermo-visco-elastic medium

The problem of wave propagation in an interacting random infinite magneto-thermo-visco-elastic medium has been studied formulating a generalised theory of thermoelasticity recently proposed by Noda, Furuk-Awa and Ashida [1] that combines both the generalised theories developed by Lord and Shulman [2] as well as by Green and Lindsay [3]. The perturbation technique relevant to stochastic differential equations has been employed to obtain the relation connecting displacement amplitudes of waves propagating in the interacting media. The appropriate Greenʹs tensor essential for the discussion has been obtained in the course of analysis. A more general coupled dispersion relation for longitudinal and transverse waves has been deduced to determine the effect of visco-elasticity, relaxation times, and rotation on the phase velocity of the coupled waves. The equations have been analysed for a particular form of thermo-mechanical coupling and autocorrelation function to show that the effect (of the order of ε2 only) of the thermal field is to attenuate the longitudinal type waves and to alter the phase-speed depending upon the values of the visco-elastic parameters, relaxation times, and rotation. Cases of low and high frequencies have also been studied, and numerical calculations have been done to determine the effect of visco-elastic parameters, relaxation times, rotation, and thermoelastic coupling on the phase velocity and attenuation coefficient of the waves.