Wave propagation in the two temperature theory of thermoelasticity

Warren, William E.; Chen, P. J.

doi:10.1007/bf01177123

Cited by 196 publications

(87 citation statements)

References 3 publications

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“…The two temperatures, T and ϕ, and the strain are found to have representations in the form of a traveling wave plus a response, which occurs instantaneously throughout the body [Boley and Tolins 1962]. Warren and Chen [1973] investigated the wave propagation in the two-temperature theory of thermoelasticity. In [Youssef 2006b] we investigated this theory in the context of the generalized theory of thermoelasticity.…”

Section: P J Chen and Collaboratorsmentioning

confidence: 99%

A two-temperature generalized thermoelastic medium subjected to a moving heat source and ramp-type heating: A state-space approach

Youssef¹

2010

JOMMS

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We construct a model of two-temperature generalized thermoelasticity for an elastic half-space with constant elastic parameters. The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to the specific problem of a half-space subjected to a moving heat source with constant velocity and ramp-type heating. The inverse Laplace transforms are computed numerically. The effects of different values of the heat source velocity, the two-temperature parameter, and the ramping time parameter are compared.A list of symbols can be found on page 1648.

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Section: P J Chen and Collaboratorsmentioning

confidence: 99%

A two-temperature generalized thermoelastic medium subjected to a moving heat source and ramp-type heating: A state-space approach

Youssef¹

2010

JOMMS

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“…The two temperatures T, and the strain are found to have representations in the form of a traveling wave plus a response, which occur instantaneously throughout the body [4]. Warren and Chen [5] investigated the wave propagation in the twotemperature theory of thermoelasticity, but Youssef [7] investigated this theory in the context of generalized thermoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Two Temperature Thermo-Elastic Behavior of Piezoelectric Materials

Bassiouny¹,

Sabry²

2013

JAMP

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A new mathematical model of time fractional order heat equation and fractional order boundary condition have been constructed in the context of the generalized theory of thermo piezoelasticity. The governing equations have been applied to a semi infinite piezoelectric slab. The Laplace transform technique is used to remove the time-dependent terms in the governing differential equations and the boundary condition. The solution of the problem is first obtained in the Laplace transform domain. Furthermore, a complex inversion formula of the transform based on a Fourier expansion is used to get the numerical solutions of the field equations which are represented graphically.

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“…The main difference of this theory with respect to the classical one is in the thermal dependence. The theory was proposed by Chen, Gurtin and Williams (see [1], [3], [6]) and several authors have dedicate its attention to this problem (Ieşan [7], Chen et al [2], [16], Quintanilla [11], [12], among others). In this paper where elastic effects are taken into consideration we deal with the two models proposed by Youssef [18].…”

Section: Introductionmentioning

confidence: 99%

On (non-)exponential decay in generalized thermoelasticity with two temperatures

Leseduarte

Quintanilla

Racke

2017

Applied Mathematics Letters

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Wave propagation in the two temperature theory of thermoelasticity

Cited by 196 publications

References 3 publications

A two-temperature generalized thermoelastic medium subjected to a moving heat source and ramp-type heating: A state-space approach

A two-temperature generalized thermoelastic medium subjected to a moving heat source and ramp-type heating: A state-space approach

Fractional Order Two Temperature Thermo-Elastic Behavior of Piezoelectric Materials

On (non-)exponential decay in generalized thermoelasticity with two temperatures

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