A generalized linear thermoelasticity theory for piezoelectric media

Chandrasekharaiah, D. S.

doi:10.1007/bf01173936

Cited by 207 publications

(71 citation statements)

References 16 publications

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“…The physical laws for the thermopiezoelectric material have been explored by Nowacki [3,4]. Chandrasekharaiah [5] used generalised Mindlin's theory of thermopiezoelectricity to account for the finite speed of propagation of thermal disturbances.…”

Section: Introductionmentioning

confidence: 99%

Modelling of Piezothermoelastic Beam with Fractional Order Derivative

Kumar¹,

Sharma²

2016

Curved and Layered Structures

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This paper deals with the study of transverse vibrations in piezothermoelastic beam resonators with fractional order derivative. The fractional order theory of thermoelasticity developed by Sherief et al. [1] has been used to study the problem. The expressions for frequency shift and damping factor are derived for a thermo micro-electromechanical (MEM) and thermo nano-electromechanical (NEM) beam resonators clamped on one side and free on another. The effect of fractional order derivative on the derived expressions is observed analytically and shown graphically in the case of Lead Zirconate Titanate (PZT)-5A material. For α = 1, our results agree with those that are obtained by Grover and Sharma [20] and other particular cases of interest are also discussed.

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Section: Introductionmentioning

confidence: 99%

Modelling of Piezothermoelastic Beam with Fractional Order Derivative

Kumar¹,

Sharma²

2016

Curved and Layered Structures

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“…In fact, the thermo-electro-elastic coupling problems have been studied by many researchers in the past decades [1][2][3][4][5]. More recently, Gao et al [6] derived the exact solution for the problem of an elliptical hole or a crack in a thermopiezoelectric solid by using the complex variable method.…”

Section: Introductionmentioning

confidence: 99%

The Generalized Two Dimensional Thermal-Electro-Elastic Solution for the Cracked-Half-Elliptical-Hole Problem in a Half Plane

Wang¹,

Gao²,

Song³

et al. 2015

Journal of Theoretical and Applied Mechanics

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Abstract. The half elliptical hole with an edge crack in a thermopiezoelectric material is studied by using the complex variable method. First, the mapping function which maps the outside of the elliptical hole and the crack in the right half plane into the outside of a circular hole in a full plane is given by the method of conformal mapping. Then, the complex potential functions and the field intensity factors (FIF) are presented according to the boundary conditions, respectively. Some useful results can be found by numerical analysis: 1) The influence of the heat flux on FIF depends on the model of the crack; 2) The shape and the size of the hole possess a significant effect on the field distribution at the crack tip.

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“…General models for elastic materials with thermopiezoelectric effects can be found in [4,11,14] and, more recently, in [1]. Some theoretical results for static frictional contact models taking into account the interaction between the electric and the mechanic fields have been obtained in [3,8,9,12], under the assumption that the foundation is insulated, and in [5,6,10] under the assumption that the foundation is electrically conductive.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Signorini problem with nonlocal friction in thermo-piezoelectricity

Benaissa

Essoufi

Fakhar

2016

Glas. Mat. Ser. III

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Abstract. We consider a mathematical model which describes the frictional unilateral contact between a thermo-piezoelectric body and a rigid electrically conductive foundation. The thermo-piezoelectric constitutive law is assumed to be nonlinear and the contact is modeled with the Signorini condition, the nonlocal Coulomb friction law with slip dependent friction coefficient and the regularized electrical and thermal conductivity conditions. The variational form of this problem is a coupled system which consists of a nonlinear variational inequality for the displacement field and two nonlinear variational equations for the electric potential and the temperature. The existence of a unique weak solution to the problem is proved by using abstract results for elliptic variational inequalities and fixed point arguments.

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A generalized linear thermoelasticity theory for piezoelectric media

Cited by 207 publications

References 16 publications

Modelling of Piezothermoelastic Beam with Fractional Order Derivative

Modelling of Piezothermoelastic Beam with Fractional Order Derivative

The Generalized Two Dimensional Thermal-Electro-Elastic Solution for the Cracked-Half-Elliptical-Hole Problem in a Half Plane

Analysis of a Signorini problem with nonlocal friction in thermo-piezoelectricity

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