Eigenfunction expansion method to the solution of simultaneous equations and its application in mechanics

Das, Narayan Chandra; Bhakta, P. C.

doi:10.1016/0093-6413(85)90030-8

Cited by 32 publications

(5 citation statements)

References 3 publications

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“…From Eqs. (25) and (26), the eigenvector corresponding to the eigenvalue = , = 1, 2, 3, 4 can be easily calculated. The following notations will be used:…”

Section: Solution Of the Vector Matrix Differential Equationmentioning

confidence: 99%

“…Some applications of magneto thermorelasticity using eigenvalue approach technique were examined in the literatures [24,25]. Das and Bhakata [26] proposed eigenfunction expansion technique to the solution of simultaneous equations and its application in mechanics. Baksi et al [27] examined magneto-thermoelastic interactions with heat sources and thermal relaxation in a three dimensional unbounded rotating elastic medium.…”

Section: Introductionmentioning

confidence: 99%

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Thermal shock behaviour on generalized thermoelastic semi-infinite medium with moving heat source under Green Naghdi-III model

Singh¹,

Pal²

2019

Math. models, eng.

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The present article deals with the thermal shock response in an isotropic thermoelastic medium with a moving heat source. In this context Green and Naghdi type III model of generalized thermoelasticity theory is considered. The basic equations are expressed as vector-matrix differential equation form. The considered formulation is applied to a semi-infinite solid space. The analytical formulations of the problem in the Laplace transform domain have been solved by eigenvalue approach technique. The inversion of Laplace transform is completed by Zakian method. The variation of the temperature, displacement and stress distributions for different values of time and heat source velocity are shown graphically for two different cases. In the first case, a thermal shock free surface is considered subjected to traction and in the second case the surface is under the influence of time dependent thermal shock. Finally, some comparisons of the results for different time and moving heat source velocity are presented. In presence of moving heat source all the thermophysical quantities have a great significant effect in all the distributions.

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“…From Eqs. (25) and (26), the eigenvector corresponding to the eigenvalue = , = 1, 2, 3, 4 can be easily calculated. The following notations will be used:…”

Section: Solution Of the Vector Matrix Differential Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermal shock behaviour on generalized thermoelastic semi-infinite medium with moving heat source under Green Naghdi-III model

Singh¹,

Pal²

2019

Math. models, eng.

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“…Following the solution methodology through eigenvalue approach [18,28,29], we now proceed to solve the vector-matrix differential equation (29). The characteristic equation of the matrix is…”

Section: Eigenvalue Approachmentioning

confidence: 99%

“…The problem has been solved numerically using the normal mode analysis [19,[25][26][27][28] together with the eigenvalue approach [28,29]. Numerical results for the conductive temperature, thermodynamic temperature, displacement components and the stresses are represented graphically and the results are analyzed.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Gravity Field on the Plane Waves in a Fiber-Reinforced Two-Temperature Magneto-Thermoelastic Medium Under Lord-Shulman Theory

Sarkar

Lahiri

2013

Journal of Thermal Stresses

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The aim of the present work is to investigate the influence of the gravity field on the plane waves in a linearly fiber-reinforced magneto-thermoelastic isotropic medium in the context of the two-temperature theory of generalized thermoelasticity under Lord-Shulman model. The problem has been solved numerically using the normal mode analysis together with the eigenvalue approach. Numerical results for the conductive temperature, thermodynamic temperature, displacement components and the stresses are represented graphically and the results are analyzed. The graphical results indicate that the effect of the two-temperature parameter, gravity field and the magnetic field on the plane waves in the fiber-reinforced thermoelastic medium are very pronounced. Comparisons are made with the results in the presence and absence of the two-temperature parameter, gravity field and the magnetic field. Such problems are very important in many dynamical systems.

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“…The problem has been solved numerically using the normal mode analysis [13,[19][20][21][22] together with the eigenvalue approach [22,23]. Numerical results for the temperature, the displacement components and the stresses are represented graphically and analyze the results.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Magnetothermoelastic Response in a Fiber-Reinforced Elastic Solid Due to Hydrostatic Initial Stress and Gravity Field

Sarkar

2014

Journal of Thermal Stresses

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The aim of the present paper is to investigate the influences of the hydrostatic initial stress and the gravity field on the plane waves in a fiber-reinforced magnetothermoelastic isotropic medium using the Lord-Shulman model of generalized thermoelasticity with one relaxation time. The problem has been solved numerically using the normal mode analysis together with the eigenvalue approach. Numerical results for temperature, the displacement components, and the stresses are represented graphically, and the results are analyzed. The graphical results indicate that the effects of the hydrostatic initial stress, gravity field, and the magnetic field on plane waves in the fiber-reinforced thermoelastic medium are very pronounced. Comparisons are made to results in the absence of the hydrostatic initial stress, gravity field, and the magnetic field. Such problems are very important in many dynamical systems.

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Eigenfunction expansion method to the solution of simultaneous equations and its application in mechanics

Cited by 32 publications

References 3 publications

Thermal shock behaviour on generalized thermoelastic semi-infinite medium with moving heat source under Green Naghdi-III model

Thermal shock behaviour on generalized thermoelastic semi-infinite medium with moving heat source under Green Naghdi-III model

The Effect of Gravity Field on the Plane Waves in a Fiber-Reinforced Two-Temperature Magneto-Thermoelastic Medium Under Lord-Shulman Theory

Analysis of Magnetothermoelastic Response in a Fiber-Reinforced Elastic Solid Due to Hydrostatic Initial Stress and Gravity Field

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