BHARTI KUMARI - Academia.edu (original) (raw)

Papers by BHARTI KUMARI

The present work is concerned with thermoelasticity without the energy dissipation theory for a p... more The present work is concerned with thermoelasticity without the energy dissipation theory for a problem of an infinitely long and isotropic annular cylinder of temperature dependent physical properties. We employ the thermoelasticity theory of GN-II and derive the basic governing equations with variable material properties. The formulation is then applied to solve a boundary value problem of an annular cylinder with its inner boundary assuming to be stress free and subjected to exponential decay in temperature and sinusoidal temperature distribution. The outer boundary is also assumed to be stress free and is maintained at reference temperature in both cases. We solve the non-linear coupled differential equations by applying the finite difference approach efficiently. We analyze the numerical results in a detailed way with the help of different graphs. The effects of temperature dependency of material properties on the thermo-mechanical responses for two different time dependent temperature distributions applied at the inner boundary are highlighted.

Mathematics and Mechanics of Solids, Aug 1, 2016

The present work is concerned with the thermoelasticity theory of Green and Naghdi of type I, II ... more The present work is concerned with the thermoelasticity theory of Green and Naghdi of type I, II and III. By considering a mixed initial-boundary value problem for an isotropic medium in the context of all three models of type I, II and III in a unified way, we derive an identity in terms of the temperature and potential. On the basis of this identity, we establish the domain of influence theorem for the Green–Naghdi-II model. This theorem implies that for a given bounded support of thermomechanical loading, the thermoelastic disturbance generated by the pair of temperature and potential of the system vanishes outside a well-defined bounded domain. This domain is shown to depend on the support of the load, that is, on the initial and boundary data. It is also shown that under Green–Naghdi-II model, the thermoelastic disturbance propagates with a finite speed that is dependent on the thermoelastic parameters.

In this work, we study the thermoelastic interactions in an unbounded medium with a spherical cav... more In this work, we study the thermoelastic interactions in an unbounded medium with a spherical cavity in the context of a very recently proposed heat conduction model established by Quintanilla (2011). This model is a reformulation of three-phase-lag conduction model and is an alternative heat conduction theory with a single delay term. We make an attempt to study the thermoelastic interactions in an isotropic elastic medium with a spherical cavity subjected to three types of thermal and mechanical loads in the contexts of two versions of this new model. Analytical solutions for the distributions of the field variables are found out with the help of the integral transform technique. A detailed analysis of analytical results is provided by short-time approximation concept. Further, the numerical solutions of the problems are obtained by applying numerical inversion of Laplace transform. We observe significant variations in the analytical results predicted by different heat conduction ...

Mathematics and Mechanics of Solids, 2018

This work is concerned with a recent thermoelastic model. We investigate the propagation of plane... more This work is concerned with a recent thermoelastic model. We investigate the propagation of plane harmonic waves in the context of this very recently proposed heat conduction model, an exact heat conduction model with a single delay term, established by Quintanilla. This model attempted to reformulate the heat conduction model that takes into account microstructural effects in heat transport phenomena and provided an alternative heat conduction theory with a single delay term. We aim to study the harmonic plane waves propagating in a thermoelastic medium by employing this new model and derive the exact dispersion relation solution. We mainly focus on a longitudinal wave coupled to a thermal field and find two different modes of this wave. We derive asymptotic expressions for several important characterizations of the wave fields: phase velocity, specific loss, penetration depth, and amplitude ratio. Analytical expressions for these wave characteristics are obtained for different cas...

Journal of Thermal Stresses, 2017

The present work is concerned with the thermoelasticity theory based on a very recently proposed ... more The present work is concerned with the thermoelasticity theory based on a very recently proposed heat conduction model-a heat conduction model with a delay term introduced by Quintanilla. Here we aim to obtain the fundamental solutions of thermoelasticity in the context of this theory. We derive the solution of Galerkin-type eld equations for the case of homogeneous and isotropic bodies. With the help of this solution, we determine the e ects of concentrated heat sources and body forces in an unbounded medium. We further obtain the fundamental solutions of the eld equations in case of steady vibrations.

Mathematics and Mechanics of Solids, 2016

The present work is concerned with a very recently proposed heat conduction model—an exact heat c... more The present work is concerned with a very recently proposed heat conduction model—an exact heat conduction model with a delay term for an anisotropic and inhomogeneous material—and some important theorems within this theory. A generalized thermoelasticity theory was proposed based on the heat conduction law with three phase-lag effects for the purpose of considering the delayed responses in time due to the micro-structural interactions in the heat transport mechanism. However, the model defines an ill-posed problem in the Hadamard sense. Subsequently, a proposal was made to reformulate this constitutive equation of heat conduction theory with a single delay term and the spatial behavior of the solutions for this theory have been investigated. A Phragmen–Lindelof type alternative was obtained and it has been shown that the solutions either decay in an exponential way or blow-up at infinity in an exponential way. The obtained results are extended to a thermoelasticity theory by consid...

Journal of Thermal Stresses, 2016

The present paper is focused on the Moore-Gibson-Thompson (MGT) thermoelasticity theory. The MGT ... more The present paper is focused on the Moore-Gibson-Thompson (MGT) thermoelasticity theory. The MGT thermoelasticity theory is a generalized form of the Lord-Shulman (LS) thermoelasticity theory as well as the Green-Naghdi thermoelasticity theory with energy dissipation (GN-III). The present work is aimed at establishing the domain of influence results in the context of this new thermoelasticity theory. We consider a mixed boundary-initial value problem representing natural stress-heat-flux disturbance inside an isotropic and homogeneous medium. We establish an identity regarding this present problem. Further, we derive the domain of influence theorem based on this identity under the MGT thermoelasticity theory. From this theorem, we conclude that for prescribed bounded support of thermomechanical loading and for a finite time, the disturbance generated by the pair of stress and heat flux vanishes outside a bounded domain. It is also analyzed that the domain of influence relies on the thermoelastic material parameters. We further compare the present domain of influence results with the corresponding results of LS thermoelasticity theory.