Free Vibrations of a Linear Thermopiezoelectric Body

Yang, Jiashi; Batra, R.C.

doi:10.1080/01495739508946301

Cited by 40 publications

(7 citation statements)

References 14 publications

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“…In this work the following linear constitutive relations for thermopiezoelectric materials are employed [12]: Hamilton's principle is employed here to derive the finite element equations:…”

Section: Basic Equations and Fe Methods Implementationmentioning

confidence: 99%

Thermoelastic and Pyroelectric Couplings Effects on Dynamics and Active Control of Smart Piezolaminated Beam Modeled by Finite Element Method

Sanbi

Saadani²,

Sbai³

et al. 2014

Smart Materials Research

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Smart structures with integrated sensors, actuators, and control electronics are of importance to the next generation highperformance structural systems. In this study, thermopiezoelastic characteristics of piezoelectric beam continua are studied and applications of the theory to active structures in sensing and optimal control are discussed. Using linear thermopiezoelastic theory and Timoshenko assumptions, a generic thermopiezoelastic theory for piezolaminated composite beam is derived. Finite element equations for the thermopiezoelastic media are obtained by using the linear constitutive equations in Hamilton's principle together with the finite element approximations. The structure consists of a modeling of cantilevered piezolaminated Timoshenko beam with integrated thermopiezoelectric elements between two aluminium layers. The structure is modelled analytically and then numerically and the results of simulations are presented in order to visualize the states of their dynamics and the state of control. The optimal control LQG accompanied by the Kalman filter is applied. The effects of thermoelastic and pyroelectric couplings on the dynamics of the structure and on the control procedure are studied and discussed. We show that the control procedure cannot be perturbed by applying a thermal gradient and the control can be applied at any time during the period of vibration of the beam.

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“…In this work the following linear constitutive relations for thermopiezoelectric materials are employed [12]: Hamilton's principle is employed here to derive the finite element equations:…”

Section: Basic Equations and Fe Methods Implementationmentioning

confidence: 99%

Thermoelastic and Pyroelectric Couplings Effects on Dynamics and Active Control of Smart Piezolaminated Beam Modeled by Finite Element Method

Sanbi

Saadani²,

Sbai³

et al. 2014

Smart Materials Research

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show abstract

“…Considering thermopiezoelastic material, the constitutive equations of linear thermopiezoelasticity and temperature are written as [12] …”

Section: Basic Equations and Fem Implementationmentioning

confidence: 99%

Thermal Effects on Vibration and Control of Piezocomposite Kirchhoff Plate Modeled by Finite Elements Method

Sanbi

Saadani

Sbai

et al. 2015

Smart Materials Research

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Theoretical and numerical results of the modeling of a smart plate are presented for optimal active vibration control. The smart plate consists of a rectangular aluminum piezocomposite plate modeled in cantilever configuration with surface bonded thermopiezoelectric patches. The patches are symmetrically bonded on top and bottom surfaces. A generic thermopiezoelastic theory for piezocomposite plate is derived, using linear thermopiezoelastic theory and Kirchhoff assumptions. Finite element equations for the thermopiezoelastic medium are obtained by using the linear constitutive equations in Hamilton's principle together with the finite element approximations. The structure is modelled analytically and then numerically and the results of simulations are presented in order to visualize the states of their dynamics and the state of control. The optimal control LQGKalman filter is applied. By using this model, the study first gives the influences of the actuator/sensor pair placement and size on the response of the smart plate. Second, the effects of thermoelastic and pyroelectric couplings on the dynamics of the structure and on the control procedure are studied and discussed. It is shown that the effectiveness of the control is not affected by the applied thermal gradient and can be applied with or without this gradient at any time of plate vibrations.

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“…In deriving the equations of state, we assume that the total strain ij ε includes elastic (or, in general case, viscoelastic), , and inelastic, , strain components. The constitutive equations for linear piezoelectric materials without pyroeffect can be written in the following form [19]:…”

Section: Approach Based On the Theory Of Layered Beams And The Unifiementioning

confidence: 99%

“…These equations were derived in the electrostatic approximation, i.e., the equations of electrostatics [2,19] are assumed to be true. The Bodner-Partom model was used to simulate the inelastic response of the electrically passive material (aluminium alloy) [12].…”

Section: Approach Based On the Theory Of Layered Beams And The Unifiementioning

confidence: 99%

Vibration analysis of thin-wall structures containing piezoactive layers

Guz

Zhuk

Kashtalyan

2010

IOP Conf. Ser.: Mater. Sci. Eng.

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Free Vibrations of a Linear Thermopiezoelectric Body

Cited by 40 publications

References 14 publications

Thermoelastic and Pyroelectric Couplings Effects on Dynamics and Active Control of Smart Piezolaminated Beam Modeled by Finite Element Method

Thermoelastic and Pyroelectric Couplings Effects on Dynamics and Active Control of Smart Piezolaminated Beam Modeled by Finite Element Method

Thermal Effects on Vibration and Control of Piezocomposite Kirchhoff Plate Modeled by Finite Elements Method

Vibration analysis of thin-wall structures containing piezoactive layers

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