Santwana Mukhopadhyay

EFFECT OF ROTATION AND RELAXATION TIMES ON PLANE WAVES IN GENERALIZED THERMO-VISCO-ELASTICITY

The generalized dynamical theory of thermo-elasticity proposed by Green and Lindsay is applied to study the propagation of harmonically time-dependent thermo-visco- elastic 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

EFFECTS OF THERMAL RELAXATIONS ON THERMOVISCOELASTIC INTERACTIONS IN AN UNBOUNDED BODY WITH A SPHERICAL CAVITY SUBJECTED TO A PERIODIC LOADING ON THE BOUNDARY

Thermoviscoelastic interactions in an infinite homogeneous viscoelastic medium with a spherical cavity are studied. The cavity surface is subjected to a periodic loading and zero temperature change. The classical dynamical theory of thermoelasticity as well as the generalized theories of thermoelasticity are applied to consider the thermoelastic coupling. The analytical expressions for the closed-form solutions of displacement, temperature, and stresses are obtained; and the thermal relaxation effects on the interactions are studied to compare the three theories. The numerical values of the physical quantities are computed for a suitable material. The results are presented graphically to illustrate the problem.

Thermoelastic Interactions on Two-Temperature Generalized Thermoelasticity in an Infinite Medium with a Cylindrical Cavity

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.

Thermoelastic interactions without energy dissipation in an unbounded body with a spherical cavity subjected to harmonically varying temperature

Abstract The present work is concerned with the thermally induced vibration in a homogeneous and isotropic unbounded body with a spherical cavity. The Green and Nagdhi model of thermoelasticity without energy dissipation is employed. The closed form solutions for distributions of displacement, temperature and stresses are obtained. The solutions valid in the case of small frequency are deduced and the results are compared with the corresponding results obtained in other generalized thermoelasticity theories. Numerical results applicable to a copper-like material are also presented graphically and the nature of variations of the physical quantities with radial coordinate and with frequency of vibration is analyzed.

Variational and Reciprocal Principles in Two-Temperature Generalized Thermoelasticity

The aim of the present work is to establish a variational principle of convolutional type and a reciprocal principle in the context of linear theory of two-temperature generalized thermoelasticity, for a homogeneous and isotropic body.

Thermoelastic interactions without energy dissipation in an unbounded medium with a spherical cavity due to a thermal shock at the boundary

Thermoelastic interactions without energy dissipation in an unbounded elastic medium with a spherical cavity have been investigated. The cavity surface is assumed to be stress free and is subjected to a thermal shock. The solutions for displacement, temperature, and stresses are obtained using the Laplace transform procedure. The discontinuities of the distributions of the physical quantities are determined and compared with earlier findings. The inversions are also carried out with a numerical method based on Fourier series expansions of functions. The results are compared with the corresponding results obtained in cases of conventional thermoelasticity theory and the generalized theories of thermoelasticity with thermal relaxation time parameters.

Study of harmonic plane waves in rotating thermoelastic media of type III

In the present paper we analyze the effects of rotation on the propagation of harmonic plane waves in an unbounded type III thermoelastic media rotating with a uniform angular velocity. Exact analytical solutions of the dispersion relation equations for purely shear and purely dilatational plane waves are obtained after developing the mathematical model. Special cases of very low- and high-frequency values are considered to find the asymptotic expressions of several important characterizations associated with the plane waves propagating inside the medium. Numerical values of the wave characterizations for intermediate values of frequency for varying conductivity rates and varying angles of rotation are also obtained and are plotted graphically. A detailed analysis of the effects of rotation on the propagation of plane waves is presented on the basis of our analytical and numerical results.

A Problem on Elastic Half Space Under Fractional Order Theory of Thermoelasticity

The present work is concerned with the solution of a problem on fractional order theory of thermoelasticity for an elastic medium. We investigate the thermoelastic interactions inside the medium by employing the fractional order theory of thermoelasticity, recently advocated by Sherief et al. (Int. J. Solids Struct., 47, 269–275, 2010). State space approach together with the Laplace transform technique is used to obtain the general solution of the problem. The general solution is then applied to three specific problems on an elastic half space, whose boundary is subjected to (i) a thermal shock (i.e., a step input in temperature and zero stress), (ii) a normal load (i.e., a step input in stress and zero temperature change) and (iii) a ramp type increase in temperature and zero stress. To observe the variations of displacement, temperature and stress inside the half-space we compute the numerical values of the field variables for a particular material by utilizing a numerical method of Laplace inversion. The effects of fractional order parameter on the variations of different fields inside the medium are analyzed graphically.

EFFECTS OF THREE-PHASE-LAGS ON GENERALIZED THERMOELSTICITY FOR AN INFINITE MEDIUM WITH A CYLINDRICAL CAVITY

The present work is concerned with the effects of three-phase lags on thermoelastic interactions due to step input in temperature on the stress free boundary of a cylindrical cavity in an unbounded medium. The problem is studied in the context of theory of generalized thermoelasticity with three phase lags (Roychoudhuri, [24]) and the theory of thermoelasticity with energy dissipation (Green and Naghdi, [4]) in a unified way. Solution of the problem is obtained by using the Laplace transform technique. Significant dissimilarities between two models showing the effects of phase lags are pointed out on the basis of analytical as well as numerical results of the problem. A numerical method for the inversion of Laplace transform is employed.

A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity

The aim of the present paper is to study the thermoelastic interactions in an unbounded elastic medium with a spherical cavity in the context of four different theories of thermoelasticity, namely: the classical coupled dynamical thermoelasticity, the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation in a unified way. The cavity surface is assumed to be stress free and is subjected to a smooth and time-dependent-heating effect. The solutions for displacement, temperature and stresses are obtained with the help of the Laplace transform procedure. Firstly the short-time approximated solutions for four different theories have been obtained analytically. Then following the numerical method proposed by Bellman et al. [R. Bellmen, R.E. Kolaba, J.A. Lockette, Numerical Inversion of the Laplace Transform, American Elsevier Pub. Co., New York, 1966] for the inversion of Laplace transforms, the numerical values of the physical quantities are also computed for the copper material and results are displayed in graphical forms to compare the results obtained for the theory of thermoelasticity without energy dissipation with the results of other thermoelasticity theories.