Two-Temperature Generalized Thermopiezoelasticity for One Dimensional Problems – State Space Approach

Youssef, Hamdy M.; Bassiouny, E.

doi:10.12921/cmst.2008.14.01.55-64

Cited by 20 publications

(9 citation statements)

References 18 publications

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“…In the absence of body force, free charge and inner heat sources, we consider generalized thermo-piezoelectric governing differential equations Youssef [29] and Youssef and Bassiouny [30] follows:…”

Section: Governing Equationsmentioning

confidence: 99%

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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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Section: Governing Equationsmentioning

confidence: 99%

“…Substituting from Equation (26) into Equations (19)- (25) and dropping the primes for convenience, we obtain the following set of non-dimensional equations Youssef [29] and Youssef and Bassiouny [30] follows:…”

Section: T T U C U T C T T T T C T X C X C Tmentioning

confidence: 99%

Fractional Order Two Temperature Thermo-Elastic Behavior of Piezoelectric Materials

Bassiouny¹,

Sabry²

2013

JAMP

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“…For computational purposes, the values of the material constants have been taken as follows [52] F 0 = 1, = 0.003887, α = 0.036991, ω = 0.1, K * = 7 Here in this paper, we have considered 3P model. Now for this model, the solution of the heat conduction law is stable if where τ * ν = K * τ ν + K [32].…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The uniqueness of the solution of the last theory has been derived also from Youssef [51]. Youssef and Bassiouny [52] solved a boundary value problem of a one-dimensional piezoelectric half-space by heating its boundary using different types of heating by using two-temperature generalized theory in the context of the LS model. Youssef and El-bary [53] solved a generalized thermoelastic infinite layer problem subjected to ramp type thermal and mechanical loading under three theories.…”

Section: Introductionmentioning

confidence: 99%

One-dimensional problem of a fractional order two-temperature generalized thermo-piezoelasticity

Islam

Kanoria

2013

Mathematics and Mechanics of Solids

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This paper is concerned with the determination of the thermoelastic stress, strain and conductive temperature in a piezoelastic half-space body in which the boundary is stress free and subjected to thermal loading in the context of the fractional order two-temperature generalized thermoelasticity theory (2TT). The two-temperature three-phase-lag (2T3P) model, two-temperature Green-Naghdi model III (2TGNIII) and two-temperature Lord-Shulman (2TLS) model of thermoelasticity are combined into a unified formulation introducing unified parameters. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain that is then solved by the state-space approach. The numerical inversion of the transform is carried out by a method based on Fourier series expansion techniques. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. The effect of the fractional order parameter, two-temperature and electric field on the solutions has been studied and comparisons among different thermoelastic models are made.

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“…Youssef and Bassiouny [13] solved the boundary value problem of one dimension in two-temperature generalized thermopiezoelastic half space, subjected to the thermal shock by using state space approach.…”

Section: Introductionmentioning

confidence: 99%

Effect of Two Temperatures on Reflection Coefficient in Micropolar Thermoelastic with and without Energy Dissipation Media

Kumar

Sharma²,

Garg

2014

Advances in Acoustics and Vibration

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The reflection of plane waves at the free surface of thermally conducting micropolar elastic medium with two temperatures is studied. The theory of thermoelasticity with and without energy dissipation is used to investigate the problem. The expressions for amplitudes ratios of reflected waves at different angles of incident wave are obtained. Dissipation of energy and two-temperature effects on these amplitude ratios with angle of incidence are depicted graphically. Some special and particular cases are also deduced.

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Two-Temperature Generalized Thermopiezoelasticity for One Dimensional Problems – State Space Approach

Cited by 20 publications

References 18 publications

Fractional Order Two Temperature Thermo-Elastic Behavior of Piezoelectric Materials

Fractional Order Two Temperature Thermo-Elastic Behavior of Piezoelectric Materials

One-dimensional problem of a fractional order two-temperature generalized thermo-piezoelasticity

Effect of Two Temperatures on Reflection Coefficient in Micropolar Thermoelastic with and without Energy Dissipation Media

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