Nonlinear extension and bending of piezoelectric laminated plate under large applied field actuation

Yao, Lin‐Quan; Zhang, J G; Li, Lü; Lai, M.O.

doi:10.1088/0964-1726/13/2/019

Cited by 38 publications

(22 citation statements)

References 33 publications

(45 reference statements)

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“…The electro-mechanical interactions are widely characterized by a linear stress-strain relation (1). Nevertheless, under higher loads the experimental values differ strongly from the linear model (2), mainly due to the increasing influence of elastostriction (3) and electrostriction (4). Different authors (5,6) have addressed the issue.…”

Section: Piezoelectric Constitutive Equationsmentioning

confidence: 96%

“…The state of strain ε ij is derived by the partial derivative of expression [1] with respect to the acting stress σ ij . Utilizing the free energy for a nonlinear electro-elastic material (7) and the dielectric displacement, equation [2] can be derived. Here, s denominates the compliance, d the piezoelectric strain coefficient, κ the elastostriction effect, and a the electrostriction effect.…”

Section: Piezoelectric Constitutive Equationsmentioning

confidence: 99%

“…This basic electro-mechanical coupling in dielectric materials (13) is quadratic with the applied voltage, as seen in expression [2] and [3]. Ferroelectric materials exhibit, additionally to the field-induced polarization, a spontaneous polarization.…”

Section: Elastostrictionmentioning

confidence: 99%

See 2 more Smart Citations

Elastostriction and Electrostriction in Piezoelectric Transducers Comprising Bulk PZT Ceramics

et al. 2011

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Piezoelectric materials are a key component in applications such as sensing, actuation and energy harvesting as they couple energy between the electrical and the mechanical domain. With increasing loads, the elastostriction and the electrostriction gain impact on the PZT transducer performance. A procedure to determine the nonlinear parameters is introduced and three different PZT ceramics are studied in comparison. The detailed investigation shows that the electrostriction is dominant in actuator applications, while the elastostriction is affecting sensor applications. Piezoelectric constitutive equationsPiezoelectric materials feature the conversion of electrical energy into mechanical energy and vice versa. The electro-mechanical interactions are widely characterized by a linear stress-strain relation (1). Nevertheless, under higher loads the experimental values differ strongly from the linear model (2), mainly due to the increasing influence of elastostriction (3) and electrostriction (4). Different authors (5,6) have addressed the issue. The accuracy of these approaches is limited due to several simplifications. Further, (5) and (6) have determined two parameters from one experiment and did not consider the individual impact of each parameter. This paper gives a detailed characterization of the nonlinear parameters in bulk PZT ceramics and identifies their impact on applications for engineering, beyond the first approximation level.The volumetric electro-mechanical enthalpy H for a piezoelectric material can be written as equation [1]. U denotes the energy density, E n the electric field, and D n the electric displacement vector. n n E D U H − = [1]The state of strain ε ij is derived by the partial derivative of expression [1] with respect to the acting stress σ ij . Utilizing the free energy for a nonlinear electro-elastic material (7) and the dielectric displacement, equation [2] can be derived.

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Section: Piezoelectric Constitutive Equationsmentioning

confidence: 96%

Section: Piezoelectric Constitutive Equationsmentioning

confidence: 99%

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Elastostriction and Electrostriction in Piezoelectric Transducers Comprising Bulk PZT Ceramics

et al. 2011

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“…(1999). Yao et al. (2004b) further extended their 1D beam model to 2D piezolaminated plates using the CLT, and validated their model with the experiments of Crawley and Lazarus (1991).…”

Section: Introductionmentioning

confidence: 91%

Influence of piezoelectric nonlinearity on active vibration suppression of smart laminated shells using strong field actuation

Yasin

Kapuria

2016

Journal of Vibration and Control

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In this work, we study the effect of piezoelectric nonlinearity on shape and active vibration control of smart piezolaminated composite and sandwich shallow shells under strong field actuation. An efficient finite element model with advanced laminate kinematics and full electromechanical coupling is developed for this purpose. The nonlinearity is modeled using a rotationally invariant quadratic constitutive relationship for the piezoelectric material. For the laminate kinematics, a recently developed efficient layerwise theory, which is computationally as efficient as an equivalent single-layer theory, and has been shown to yield very accurate results in comparison with three-dimensional piezoelasticity based solutions for linear electromechanical response of hybrid laminated shells, has been employed. The nonlinear static response for shape control is obtained using the direct iteration method, and the active vibration control response with linear quadratic Gaussian controller is obtained by using the feedback linearization approach through control input transformation. It is shown that the linear model significantly overestimates the voltage required for shape or vibration control, when the applied electric field is beyond the threshold limit of the actuator. Thus, the use of the nonlinear model is essential for designing the control system utilizing the full actuation authority of the actuators. The effects of actuator thickness, radius of curvature to span ratio and applied loading on the relative difference between linear and nonlinear predictions are illustrated for shape and vibration control of smart cylindrical and spherical shells.

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“…In most of the cases described in the literature, the analytical models for nonlinear smart structures and beams adopted the polynomial constitutive relations developed by Joshi (1992) (see for example Achuthan et al, 2001;Tan and Tong, 2001;Von Wagner and Hagedorn, 2002;Sun and Tong, 2004;Yao et al, 2004;Lee et al, 2005). These polynomial constitutive relations are not valid for the levels of electromechanical loads that induce switching.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear ferro-electro-elastic beam theory

Kushnir

Rabinovitch

2009

International Journal of Solids and Structures

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a b s t r a c tMotivated by the uniqueness and potential of the nonlinear range of piezoelectric and ferroelectric smart materials and structures, a static physically nonlinear ferro-electro-elastic beam theory which takes the effect of domain switching into account is developed. The kinematic assumptions adopt the geometrically linear Bernoulli-Euler form for the mechanical components and a first-order theory for the electrical potential, and lay the basis for further augmentation to higher order theories. The beam theory includes the field equations that correspond to the static case, the boundary conditions and the constitutive equations of ferro-electro-elasticity. The general 3-D constitutive equations are reduced to comply with the beam theory and formulated as ordinary differential equations by means of a set of generalized electro-mechanical stiffnesses. A micromechanical constitutive model that accounts for the loading history and for the domain switching phenomenon is adopted and an iterative solution procedure that incorporates the micromechanical approach is suggested. A numerical example that demonstrates the impact of the domain switching on the nonlinear electromechanical static response of a ferro-electro-elastic beam is presented and discussed. The quantitative assessment of this behavior takes a step towards new structural applications that cope with or even take advantage of the nonlinear ferro-electro-elastic range.

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Nonlinear extension and bending of piezoelectric laminated plate under large applied field actuation

Cited by 38 publications

References 33 publications

Elastostriction and Electrostriction in Piezoelectric Transducers Comprising Bulk PZT Ceramics

Elastostriction and Electrostriction in Piezoelectric Transducers Comprising Bulk PZT Ceramics

Influence of piezoelectric nonlinearity on active vibration suppression of smart laminated shells using strong field actuation

Nonlinear ferro-electro-elastic beam theory

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