Eigenfunction expansion method for the solution of magneto-thermoelastic problems with thermal relaxation and heat source in three dimensions

Baksi, Arup Kumar; Bera, Rasajit Kumar

doi:10.1016/j.mcm.2005.01.032

Cited by 15 publications

(4 citation statements)

References 17 publications

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“…Problems related to the wave propagation in thermoelastic or magnetothermoelastic solids using these generalized theories have been studied by several authors (Paria [15], Das and Kanoria [16], Hsieh [17], Ezzat et al [18], Roychoudhuri [19] and Sarkar and Lahiri [20]). Problems related to magneto-thermoelasticity with thermal relaxation have been investigated by Nayfeh and Nemat-Nasser [21,22], Sherief and Youssef [23], Roychoudhuri and Chatterjee [24], Ezzat [25] and Baksi and Bera [26].…”

Section: Introductionmentioning

confidence: 99%

Magneto-thermoelastic response in a functionally graded rotating medium due to a periodically varying heat source

2015

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This paper deals with the problem of magneto-thermoelastic interactions in a functionally graded isotropic, unbounded, rotating medium due to a periodically varying heat source in the context of the linear theory of generalized thermoelasticity without energy dissipation and with energy dissipation. The governing equations of generalized thermoelasticity (GN model) for a functionally graded material under the influence of a magnetic field are established. The Laplace-Fourier double transform technique has been used to get the solution. The inversion of Fourier transform is done by using residual calculus, where the poles of the integrand are obtained numerically in the complex domain by using Laguerre's method, and the inversion of the Laplace transformation is done numerically using a method based on Fourier series expansion technique. The numerical estimates for displacements, temperature and stress are obtained for a hypothetical material. The solution to the analogous problem is obtained by taking a suitable non-homogeneous parameter. Finally, the results obtained are presented graphically to show the effect of rotation, non-homogeneity, damping coefficient and magnetic field on displacements, temperature and stress.

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Section: Introductionmentioning

confidence: 99%

Magneto-thermoelastic response in a functionally graded rotating medium due to a periodically varying heat source

2015

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“…Green‐Lindsay (G‐L, 1972) deduced another theory known as temperature wave‐dependent theory of thermo‐elasticity which includes the rate of temperature in the constituting equations. Baksi and Bera (2005), Banerjee and Roychoudhuri (1995), Chandrasekharaiah (1996) and Chakraborty (1998) utilized Lord and Shulman (1967) theory to study their problems. Roy Choudhuri and Chatterjee (1990) used G‐L (1972) theory in their problems.…”

Section: Introductionmentioning

confidence: 99%

“…Nayfeh and Nemat‐Nasser (1972) studied the problem of transient wave in thermally relaxing solids. Baksi and Bera (2005) utilized eigen function method to find the solution of magneto‐thermo‐elastic problem with relaxation and heat source in three dimension. Magneto‐thermo‐visco elastic wave propagation with reflection and refraction of the plane wave at the interface between two micropolar media has been investigated by Song and Zhang (2006).…”

Section: Introductionmentioning

confidence: 99%

Transient thermo‐elastic disturbances in a visco‐elastic semi‐space due to moving internal heat source

Lotfy

2011

International Journal of Structural Integrity

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PurposeThis paper aims to investigate the transient disturbances created by an internal line heat source that suddenly starts moving uniformly inside a visco‐elastic half‐space.Design/methodology/approachGeneralised theory of thermo‐elasticity with relaxation time proposed by Lord‐Shulman is applied. The material of the semi‐infinite medium is an isotropic visco‐elastic solid of Kelvin‐Voight type. Fourier and Laplace transform techniques are used.FindingsApplying the Fourier and Laplace transform techniques, expressions for displacement components in the transformed domain are found. These expressions prove the existence of three waves – a modified thermal wave, a visco‐elastic wave of defused nature and a transverse visco‐elastic wave.Research limitations/implicationsSurface displacement components were evaluated on the boundary for only a short time.Originality/valueThe paper provides numerical results that are illustrated graphically to highlight the variations of surface displacement components with distance for different values of time, source depth and velocity of the source.

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“…Ezzat et al [9] have studied electro-magneto-thermoelastic plane waves, with thermal relaxation in a medium of perfect conductivity. Problems related to magneto-thermoelasticity with thermal relaxation have been investigated by Sherief and Yoset [10] and by Baksi and Bera [11].…”

Section: Introductionmentioning

confidence: 99%

Magneto-thermoelastic Response in a Functionally Graded Isotropic Unbounded Medium Under a Periodically Varying Heat Source

Das

Kanoria

2009

Int J Thermophys

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This paper deals with the problem of magneto-thermoelastic interactions in a functionally graded isotropic unbounded medium due to the presence of periodically varying heat sources in the context of linear theory of generalized thermoelasticity with energy dissipation (TEWED) and without energy dissipation (TEWOED) having a finite conductivity. The governing equations of generalized thermoelasticity (GN model) for a functionally graded material (FGM) under the influence of a magnetic field are established. The Laplace-Fourier double transform technique has been used to get the solution. The inversion of the Fourier transform has been done by using residual calculus, where poles of the integrand are obtained numerically in a complex domain by using Leguerre's method and the inversion of the Laplace transformation is done numerically using a method based on a Fourier series expansion technique. Numerical estimates of the displacement, temperature, stress, and strain are obtained for a hypothetical material. The solution to the analogous problem for homogeneous isotropic materials is obtained by taking a suitable non-homogeneous parameter. Finally, the results obtained are presented graphically to show the effect of a non-homogeneous, magnetic field and damping coefficient on displacement, temperature, stress, and strain.

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Eigenfunction expansion method for the solution of magneto-thermoelastic problems with thermal relaxation and heat source in three dimensions

Cited by 15 publications

References 17 publications

Magneto-thermoelastic response in a functionally graded rotating medium due to a periodically varying heat source

Magneto-thermoelastic response in a functionally graded rotating medium due to a periodically varying heat source

Transient thermo‐elastic disturbances in a visco‐elastic semi‐space due to moving internal heat source

Magneto-thermoelastic Response in a Functionally Graded Isotropic Unbounded Medium Under a Periodically Varying Heat Source

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