Magnetoelastic plane waves in rotating media in thermoelasticity of type II (G‐N model)

Abstract

A study is made of the propagation of time-harmonic plane waves in an infinite, conducting, thermoelastic solid permeated by a uniform primary external magnetic field when the entire medium is rotating with a uniform angular velocity. The thermoelasticity theory of type II (G-N model) (1993) is used to study the propagation of waves. A more general dispersion equation is derived to determine the effects of rotation, thermal parameters, characteristic of the medium, and the external magnetic field. If the primary magnetic field has a transverse component, it is observed that the longitudinal and transverse motions are linked together. For low frequency (χ 1, χ being the ratio of the wave frequency to some standard frequency ω * ), the rotation and the thermal field have no effect on the phase velocity to the first order of χ and then this corresponds to only one slow wave influenced by the electromagnetic field only. But to the second order of χ, the phase velocity, attenuation coefficient, and the specific energy loss are affected by rotation and depend on the thermal parameters c T , c T being the nondimensional thermal wave speed of G-N theory, and the thermoelastic coupling T , the electromagnetic parameters H , and the transverse magnetic field R H . Also for large frequency, rotation and thermal field have no effect on the phase velocity, which is independent of primary magnetic field to the first order of (1/χ) (χ 1), and the specific energy loss is a constant, independent of any field parameter. However, to the second order of (1/χ), rotation does exert influence on both the phase velocity and the attenuation factor, and the specific energy loss is affected by rotation and depends on the thermal parameters c T and T , electromagnetic parameter H , and the transverse magnetic field R H , whereas the specific energy loss is independent of any field parameters to the first order of (1/χ).

One-dimensional thermoelastic waves in elastic half-space with dual phase-lag effects

“…Problems concerning generalized thermoelasticity theories and G-N theory have been studied by many authors [RoyChoudhuri and Debnath 1983;RoyChoudhuri 1984;1985;1987;Dhaliwal and Rokne 1988;RoyChoudhuri 1990;Chandrasekharaiah and Murthy 1993;Chandrasekhariah and Srinath 1996;RoyChoudhuri and Banerjee 2004;RoyChoudhuri and Bandyopadhyay 2005;RoyChoudhuri and Dutta 2005;. Tzou [1995a;1995b] and Ozisik and Tzou [1994] have developed a new model called dual phase-lag model for heat transport mechanism in which Fourier's law is replaced by an approximation to a modification of Fourier's law with two different time translations for the heat flux and the temperature gradient.…”

Propagation of plane waves in a rotating magneto-thermoelastic fiber-reinforced medium under G-N theory

“…A number of discussions relating wave propagation in rotating isotropic or anisotropic media were reported in literature, some of which are the works of RoyChoudhuri [7], Gupta and Gupta [14], Singh [24], Maity et al [16,17]. Roychoudhuri and Banerjee [8] studied the propagation of time-harmonic coupled electromagnetoelastic dilatational thermal shear waves using the thermoelasticity theory of type II (G-N model) [13]. Thermoelastic plane waves in a rotating isotropic medium has been studied by Ahmad and Khan [3].…”

Reflection of Plane Waves in Generalized Thermoelastic Half Space under the Action of Uniform Magnetic Field

“…A problem of reflection of plane waves in a rotating transversely isotropic magnetothermoelastic half space has 2 International Journal of Engineering Mathematics been discussed by Singh and Yadav [14]. Roychoudhuri and Banerjee [15] investigated viscoelastic plane waves in a rotating thermoelastic medium following Green-Naghdi model. Thermoelastic plane waves in a rotating isotropic medium have been studied by Ahmad and Khan [16].…”