Basudeb Mukhopadhyay

A thermoviscoelastic problem of an infinite medium with a spherical cavity using generalized theory of thermoelasticity

The distribution of displacements, temperature, and stresses in a homogeneous isotropic viscoelastic medium with a spherical cavity when the relaxation effect is accounted for, is considered in the context of generalized thermoelasticity. The Laplace transform technique is used and vector matrix differential method is employed to solve the problem.

Effect of distributed instantaneous and continuous heat sources in an infinite conducting magneto-thermo-viscoelastic solid with thermal relaxation

Abstract The generalised dynamical theory of thermoelasticity is applied to solve the problem of determination of the distribution of temperature, deformation, stress and strain in an infinite isotropic viscoelastic solid of Kelvin-Voigt type permeated by uniform magnetic field having distributed instantaneous and continuous heat sources. The solutions are derived by the use of Laplace transform on time and Fourier transform on space. Since the effects of relaxation time on thermo-viscoelastic interactions are short-lived, wave fronts and short time approximations are considered.

Effect of thermal relaxation on electro-magnetic-thermo-visco-elastic plane waves in rotating media

Abstract The generalised dynamical theory of thermo elasticity is applied to study the propagation of electro-magneto-thermal plane harmonic waves in an infinite isotropic conducting visco-elastic medium of Kelvin-Voigt type permeated by a primary magnetic field and rotating uniformly with constant angular velocity. The present analysis includes the thermal relaxation time of heat conduction, the electric displacement current, the coupling between heat flow density and current density and that between the temperature gradient and the electric current. To determine the effects of rotation, the relaxation time and the external magnetic field on the phase velocity of the waves, a more general dispersion equation is obtained. The discussions have centered round two cases: (A) when the external magnetic field and the axis of rotation coincide and (B) when the axis of rotation is normal to the external magnetic field with zero charge density. Perturbation technique has been used to determine the wave speed and attenuation coefficient.

Rayleigh surface wave propagation in orthotropic thermoelastic solids under three-phase-lag model

ABSTRACT The present article deals with the propagation of Rayleigh surface waves in a homogeneous, orthotropic thermoelastic half-space in the context of three-phase-lag model of thermoelasticity. The frequency equations in closed form are derived and the amplitude ratios of surface displacements and temperature change during the Rayleigh wave propagation on the surface of half-space have been computed analytically. The path of particles during Rayleigh wave propagation is found elliptical and eccentricity of the ellipse is derived. To illustrate the analytical developments, the numerical solution is performed and the computer-simulated results in respect of phase velocity, attenuation coefficient, and specific loss are presented graphically.

Periodically varying heat source response in a functionally graded microelongated medium

Abstract The present paper deals with the response due to periodically varying heat sources in the neighborhood of the origin of a functionally graded isotropic unbounded microelongated medium, in the context of generalized thermoelastic theory. The expressions for displacement, microelongation and temperature fields have been obtained in Laplace–Fourier transformed domain. After computing the inverse Fourier transforms by contour integration technique, the inversion of Laplace transforms has been obtained numerically. The changes of displacement, microelongation, and normal strain have been shown graphically for different types of heat source.

A two dimensional thermoviscoelastic problem due to instantaneous point heat source

A dynamic problem of thermoviscoelasticity in the presence of heat source is studied here. The solution in Laplace-Fourier transformed domain is obtained using eigen value approach. Stress distributions are computed numerically.

A bioeconomic model of a ratio-dependent predator-prey system and optimal harvesting

This paper deals with the problem of a ratio-dependent prey-predator model with combined harvesting. The existence of steady states and their stability are studied using eigenvalue analysis. Boundedness of the exploited system is examined. We derive conditions for persistence and global stability of the system. The possibility of existence of bionomic equilibria has been considered. The problem of optimal harvest policy is then solved by using Pontryagin’s maximal principle.

Eigenfunction expansion method to analyze thermal shock behavior in magneto-thermoelastic orthotropic medium under three theories

ABSTRACT This article is concerned with a study of thermal shock response in infinite thermoelastic medium under the purview of Lord–Shulman model, Green–Naghdi theory III, and three-phase-lag model of generalized thermoelasticity. The medium under consideration is assumed to be homogeneous, orthotropic, and thermally conducting. The fundamental equations of the two-dimensional problem of generalized thermoelasticity with three-phase-lag model in an infinite elastic medium under the influence of magnetic field are obtained as a vector–matrix differential equation form using normal mode analysis which is then solved by the Eigenfunction expansion method. Numerical results for the temperature, displacements and thermal stress distribution are presented graphically.

Study of linear isotropic micro-polar plate in an asymptotic approach

Abstract Linear micro-polar plate theory in an asymptotic approach is a two-dimensional approximation of three dimensional Cosserat theory. It was originally developed by Eringen. The current paper deals with the study of this type of plate theory with some modifications and an attempt has been made to develop a higher-order plate theory, especially third-order plate theory and to express the solution of the plate equations under that theory as a function of the solution of the equations of first-order micro-polar plate theory, which have already been well-discussed.

Thermal shock response in magneto-thermoelastic orthotropic medium with three-phase-lag model

Abstract This paper is dealing with the thermal shock response on the propagation of electro-magneto-thermoelastic disturbances in an orthotropic medium. In this context, three-phase-lag model of generalized thermoelasticity theory is considered. In presence of magnetic field as well as electric field, Maxwell’s equations are adopted to formulate the electro-magneto thermoelastic coupled governing equations. The considered formulation is applied to the half-space subjected to time-dependent thermal shock. The normal mode analysis is used to obtain the analytical expressions of the field variables. The variation of displacement, stress and temperature distribution with and without magnetic effect for various thermoelastic models are presented graphically. Finally, a comparison of the results with different models of thermoelasticity is made.