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 present paper is concerned with the theory of two temperature thermoelasticity with two phase-lags in which the theory of heat conduction in deformable bodies depends on two distinct temperatures -the conductive temperature and the thermodynamic temperature. A generalized heat conduction law with dual-phase-lag effects was proposed by Tzou (1995) for the purpose of considering the delayed response in times due to the microstructural interactions in the heat transport mechanism. Recently, Quintanilla (2008) has proposed to combine this constitutive equation with a two temperature heat conduction theory and has proved that a dual-phase-lag theory with two temperatures is a well-posed problem. In the present work we consider the basic equations concerning this dual-phase lag theory of two temperature thermoelasticity and make an attempt to establish some important theorems in this context. A uniqueness theorem has been established for a homogeneous and isotropic body. An alternative characterization of mixed boundary initial value problem is formulated and a variational principle as well as reciprocal principle have been established.
The present work is aimed at the study of thermoelastic interactions in an infinite medium with a cylindrical cavity in the context of a theory of generalized thermoelasticity in which the theory of heat conduction in deformable bodies depends on two different temperatures-conductive temperature and dynamic temperature. The cavity surface is assumed to be stress free and is subjected to a thermal shock. In order to make a comparison between the two-temperature generalized thermoelastic model and one-temperature generalized thermoelastic model the problem is formulated on the basis of two different models of thermoelasticity: namely, the Lord-Shulman model and the two temperature Lord-Shulman model in a unified way. Laplace transform technique and decoupling of coupled differential equations are used to derive the solution in transform domain which is then followed by the inversion of Laplace transform by a numerical method to obtain the solutions for field variables in the physical domain. Short-time approximated solutions in the physical domain are also obtained analytically and compared with the earlier findings. Numerical values of physical quantities are computed for copper material, and results obtained by different models are shown graphically for the illustration of the problem.
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