Symmetric Thermo-Electro-Elastic Response of Piezoelectric Hollow Cylinder Under Thermal Shock Using Lord–Shulman Theory

The response of a long hollow cylindrical vessel made from a piezoelectric material is considered in the present investigation. The piezoelectric vessel is subjected to a thermal shock on one surface. The generalized piezo-thermo-elasticity formulation of Lord and Shulman is adopted which contains a single relaxation time to consider the finite speed of temperature wave propagation. The response of the cylinder is assumed to be axi-symmetric. Three coupled equations are established as the governing equations, which are the equation of motion, the energy equation and the Maxwell equation. These equations are transformed into the dimensionless ones. With the aid of the generalized differential quadrature method, these equations are discretized in the radial direction. After that, with the aid of the Newmark time marching scheme, the temporal evolutions of the thermo-electro-elastic parameters are obtained. Novel numerical results are presented to obtain the response of the cylinder subjected to a thermal shock using the Lord and Shulman theory of thermoelasticity.

Influence of gravity and micro-temperatures on the thermoelastic porous medium under three theories

Purpose The purpose of this study is to obtain a general solution to the field equations of thermoelastic solid with voids and micro-temperatures under the gravitational field in the context of the three theories, namely, coupled theory (CT), Lord and Shulman theory and Green and Lindsay theory. Design/methodology/approach The normal mode analysis is used to obtain the exact expressions for the considered variables. Comparisons are made with the results obtained in the three theories with and without gravity. Some particular cases are also deduced from the present investigation. Findings The effect of the gravity on the displacement, the micro-temperature vector, the temperature distribution, the normal stress, the changes in the volume fraction field and the heat flux moments have been depicted graphically. Research limitations/implications Some particular cases are also deduced from the present investigation. Originality/value The results of the physical quantities have been illustrated graphically by a comparison between three different theories in the presence and absence of gravity.

Free vibration of a thermoelastic hollow cylinder with one relaxation time

The aim of this paper is to study the free vibration problem of a thermoelastic hollow cylinder in the context of the Lord and Shulman theory with one relaxation time. The eigenvalue approach is used to get the analytical solutions. The dispersion relations for the existence of various types of possible modes of vibrations are obtained. The validation of the roots for the dispersion relation is presented. The numerical results of frequency shift, natural frequency, and thermoelastic damping of vibrations have been presented graphically.

The effect of rotation in a magneto-micropolar thermoelastic layer with one relaxation time

The present investigation deals with the propagation of waves in a rotating micropolar generalized thermoelastic layer in the presence of a transverse magnetic field. The generalized theory of thermoelasticity (Lord and Shulman theory) is employed to study the problem. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacement, microrotation, and temperature distribution were also obtained. The dispersion curves (of phase velocity and attenuation coefficient) for symmetric and skew-symmetric modes are presented graphically to illustrate and compare the results to study the magnetic effect and the effect of rotation.

A Generalized Magneto-Thermoelastic Coupled Problem

two-dimensional problem in electromagneto-thermoelasticity for a thermally and electrically conducting half-space solid whose surface is subjected to a time-dependent heat is studied in the context of Lord and Shulman theory. The solid is placed in an initial magnetic field parallel to the plane boundary of the half-space. The normal mode analysis is used to obtain the exact expressions for the considered variables. The results of the considered variables are represented graphically. From the distributions it can be found the coupled effect and thermal wave effect.