No abstract

Abstract. The generalized dynamical theory of thermo-elasticity proposed by Green and Lindsay is applied to study the propagation of harmonically time-dependent thermo-viscoelastic plane waves of assigned frequency in an infinite visco-elastic solid of Kelvin-Voigt type, when the entire medium rotates with a uniform angular velocity. A more general dispersion equation is deduced to determine the effects of rotation, visco-elasticity, and relaxation time on the phase-velocity of the coupled waves. The solutions for the phase velocity and attenuation coefficient are obtained for small thermo-elastic couplings by the perturbation technique. Taking an appropriate material, the numerical values of the phase velocity of the waves are computed and the results are shown graphically to illustrate the problem.Keywords and phrases. Plane waves, rotating visco-elastic medium, generalized thermoelasticity.2000 Mathematics Subject Classification. Primary 74Dxx.1. Introduction. The classical theory of thermoelasticity is based on Fourier's law of heat conduction, which predicts an infinite speed of heat propagation. Many new theories have been proposed to eliminate this physical absurdity. Lord and Shulman [4] first modified Fourier's law by introducing into the field equations the term representing the thermal relaxation time. This modified theory is known as the generalized theory of thermoelasticity. Following Lord-Shulman's theory, several authors including Puri [7] and Nayfeh [6] studied the plane thermoelastic wave propagations. Later, Green and Lindsay [3] developed a more general theory of thermoelasticity, in which Fourier's law of heat conduction is unchanged, whereas the classical energy equation and the stress-strain temperature relations are modified by introducing two constitutive constants α and α * having the dimensions of time. Using this theory, Agarwal [1, 2] considered, respectively, thermoelastic and magneto-thermoelastic plane wave propagation in an infinite elastic medium. Later, Mukhopadhyay and Bera [5] applied the generalized dynamical theory of thermoelasticity to determine the distributions of temperature, deformation, stress and strain in an infinite isotropic visco-elastic solid of Kelvin-Voigt type permeated by uniform magnetic field having distributed instantaneous and continuous sources.Recently, attention has been given to the propagation of thermoelastic plane waves in a rotating medium. Following Lord-Shulman's theory, Puri [8], and Roychoudhuri and Debnath [10] studied plane wave propagation in infinite rotating elastic medium. Roychoudhuri [9] applied Green-Lindsay's theory to study the effect of rotation and

The theory of thermoelasticity with dual phase-lag effects is employed to study the problem of onedimensional disturbances in an elastic half-space with its plane boundary subjected to (i) a constant step input of temperature and zero stress, and (ii) a constant step input of stress and zero temperature. The Laplace transform method is used to solve the problem. Expressions for displacement, temperature and stress fields are obtained for small values of time. It is found that the solutions consist of two coupled waves both of which propagate with finite speeds and attenuation, influenced by the two delay times and thermoelastic coupling constant. The discontinuities that occur at the wave fronts are obtained. The characteristic features of the underlying theory are analyzed by comparing the results of the present analysis with their counterparts in coupled thermoelasticity theory (CTE) and in other generalized thermoelasticity theories ETE, TRDTE and TEWOED.

No 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