Eigenvalue Approach to Thermoelasticity

Das, Narayan Chandra; Das, Subhasish; Das, Bhaskar

doi:10.1080/01495738308942164

Cited by 70 publications

(40 citation statements)

References 6 publications

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“…The thermal and mechanical properties of the FGM under consideration are assumed to vary with the power of the radial coordinate variable. The eigenvalue approach due to Das et al [32] is used for the solution of the problem. Numerical solutions of the theoretical results are obtained and presented graphically.…”

Section: Introductionmentioning

confidence: 99%

Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock

Ghosh

Kanoria

2008

Appl. Math. Mech.-Engl. Ed.

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This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.

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Section: Introductionmentioning

confidence: 99%

Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock

Ghosh

Kanoria

2008

Appl. Math. Mech.-Engl. Ed.

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“…In the current paper, we have applied the eigenvalue approach which was developed in a previous study 36 to solve a problem of dual-phase-lag model on generalized magnetothermoelastic interaction in a functionally graded material in the presence of thermal shock. Laplace transforms techniques with eigenvalue approach are used to get the general solution for any set of boundary conditions.…”

Section: -29mentioning

confidence: 99%

Dual-Phase-Lag Model on Generalized Magneto-Thermoelastic Interaction in a Functionally Graded Material

Abbas¹,

Mohamed²

2017

IJAV

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In this work, we consider the problem of magneto-thermoelastic interactions in a functionally graded material (FGM) under dual-phase-lag model in the presence of thermal shock. The generalized thermoelasticity theory with one relaxation time has been employed. The material is assumed to be elastic and functionally graded (FGM) (i.e. material with spatially varying properties). The basic equations have been written in the form of a vectormatrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Stehfest method. Further, graphs have been drawn to show the effect of the nonhomogeneity parameter, magnetic field, and dual-phase-lag parameters on displacement, temperature, stress, and strain.

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“…where L ≡ 31 Abbas, 32-34, 36 and Youssef et al 35 The characteristic equation of the matrix A takes the form:…”

Section: The Exact Solution Of the Modelmentioning

confidence: 99%

Exact Solution for a Free Vibration of Thermoelastic Hollow Cylinder Under GNIII Model

Abbas¹

2016

IJAV

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The exact analytic solutions are obtained with the use of the eigenvalue approach for a free vibration problem of a thermoelastic hollow cylinder in the context of Green and Naghdi theory (GNIII). The dispersion relations for the existence of various types of possible modes of vibrations in the considered hollow cylinder are derived in a compact form and the validation of the roots for the dispersion relation is presented. To illustrate the analytic results, the numerical solution of various relations and equations has been carried out to compute the frequency, thermoelastic damping and frequency shift of vibrations in a hollow cylinder of copper material with MATHEMATICA and MATLAB software.

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Eigenvalue Approach to Thermoelasticity

Cited by 70 publications

References 6 publications

Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock

Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock

Dual-Phase-Lag Model on Generalized Magneto-Thermoelastic Interaction in a Functionally Graded Material

Exact Solution for a Free Vibration of Thermoelastic Hollow Cylinder Under GNIII Model

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