Active control of geometrically nonlinear transient vibration of composite plates with piezoelectric actuators

Gao, Jixiang; Shen, Yuhui

doi:10.1016/s0022-460x(02)01189-6

Cited by 88 publications

(36 citation statements)

References 15 publications

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“…The results reveal the nonlinear dependence between applied load and vibration amplitude and period due to membrane effects. The predicted results are in excellent agreement with those reported by Gao and Shen [2003], who used an uncoupled piezoelectric laminate theory and a four node plate finite element. Overall, the current method has accurately predicted the nonlinear dynamic response of flexible structures including the onset of dynamic mechanical buckling, as well as the stiffening effects due to tensile axial loads.…”

Section: 2supporting

confidence: 86%

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Coupled finite element for the nonlinear dynamic response of active piezoelectric plates under thermoelectromechanical loads

Varelis¹,

Saravanos²

2009

JOMMS

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A theoretical framework is presented for analyzing the coupled nonlinear dynamic behavior of laminated piezoelectric composite plates subject to high thermoelectromechanical loadings. It incorporates coupling between mechanical, electric, and thermal governing equations and encompass geometric nonlinearity effects due to large displacements and rotations. The mixed-field shear-layerwise plate laminate theory formulation is considered, thus degenerating the 3D electromechanical field to 2D nodal variables, and an eight-node coupled nonlinear plate element is developed. The discrete coupled nonlinear dynamic equations of motion are formulated, linearized, and numerically solved at each time step using the implicit Newmark scheme with a Newton-Raphson technique. Validation and evaluation cases on active laminated beams demonstrate the accuracy of the method and its robust capability to effectively predict the nonlinear dynamic response under time-dependent combined mechanical, thermal, and piezoelectric actuator loads. The results illustrate the capability of the method to simulate large amplitude vibrations and dynamic buckling phenomena in active piezocomposite plates. The influence of loading rates on the nonlinear dynamic structural response is also quantified. Additional numerical cases demonstrate the complex dynamic interactions between electrical, mechanical, and thermal buckling loads.

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Section: 2supporting

confidence: 86%

“…Gao and Shen [2003] adopted first-order shear deformation theory for analyzing the geometrical nonlinear transient vibration response of plates and their control. Yi et al [2000] applied solid elements to perform geometrically nonlinear analysis of surface bonded piezoelectric sensor wafers on plates and shells.…”

Section: Introductionmentioning

confidence: 99%

Coupled finite element for the nonlinear dynamic response of active piezoelectric plates under thermoelectromechanical loads

Varelis¹,

Saravanos²

2009

JOMMS

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“…The computation of large oscillations of homogeneous structures by coupling a nonlinear finite element analysis with a direct time integration procedure [27,28] or a harmonic balance method [29,30] is relatively well known today. The finite element modeling of nonlinear vibrations of piezoelectric structures is less common but has been treated in [31] or [32]. However, the vibratory responses of beams at the nanoscale are characterized by possible highly anharmonic steady-state response and very long transient response due to their outstanding quality factors.…”

Section: Introductionmentioning

confidence: 99%

Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS

Lazarus

Thomas

Deü

2012

Finite Elements in Analysis and Design

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a b s t r a c tThis article presents a finite element reduced order model for the nonlinear vibrations of piezoelectric layered beams with application to NEMS. In this model, the geometrical nonlinearities are taken into account through a von Ká rmá n nonlinear strain-displacement relationship. The originality of the finite element electromechanical formulation is that the system electrical state is fully described by only a couple of variables per piezoelectric patches, namely the electric charge contained in the electrodes and the voltage between the electrodes. Due to the geometrical nonlinearity, the piezoelectric actuation introduces an original parametric excitation term in the equilibrium equation. The reduced-order formulation of the discretized problem is obtained by expanding the mechanical displacement unknown vector onto the short-circuit eigenmode basis. A particular attention is paid to the computation of the unknown nonlinear stiffness coefficients of the reduced-order model. Due to the particular form of the von Ká rmá n nonlinearities, these coefficients are computed exactly, once for a given geometry, by prescribing relevant nodal displacements in nonlinear static solutions settings. Finally, the low-order model is computed with an original purely harmonic-based continuation method. Our numerical tool is then validated by computing the nonlinear vibrations of a mechanically excited homogeneous beam supported at both ends referenced in the literature. The more difficult case of the nonlinear oscillations of a layered nanobridge piezoelectrically actuated is also studied. Interesting vibratory phenomena such as parametric amplification or patch length dependence of the frequency output response are highlighted in order to help in the design of these nanodevices.

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“…34 In addition, researchers have reported promising properties for polyvinylidene fluoride (PVDF) ferroelectric polymer for sensor applications due to its low density, toughness and mechanical flexibility. 35 One of the most reported piezoelectric material is ferroelectric barium titanate (BaTiO 3 Þ which exhibits a high dielectric constant and has been widely employed in transducer applications. 36 A number of leadfree ferroelectric and piezoelectric materials have been recently explored and will be examined in this study.…”

Section: Methodsmentioning

confidence: 99%

Piezoelectric materials selection for sensor applications using finite element and multiple attribute decision-making approaches

et al. 2015

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This paper examines the selection and performance evaluation of a variety of piezoelectric materials for cantilever-based sensor applications. The finite element analysis method is implemented to evaluate the relative importance of materials properties such as Young's Modulus (E ), piezoelectric stress constants (e 31 Þ, dielectric constant ("Þ and Poisson's ratio (Þ for cantilever-based sensor applications. An analytic hierarchy process (AHP) is used to assign weights to the properties that are studied for the sensor structure under study. A technique for order preference by similarity to ideal solution (TOPSIS) is used to rank the performance of the piezoelectric materials in the context of sensor voltage outputs. The ranking achieved by the TOPSIS analysis is in good agreement with the results obtained from finite element method simulation. The numerical simulations show that K 0:5 Na 0:5 NbO 3 -LiSbO 3 (KNN-LS) materials family is important for sensor application. Young's modulus (EÞ is most influencing material's property followed by piezoelectric constant (e 31 Þ, dielectric constant ("Þ and Poisson's ratio () for cantilever-based piezoelectric sensor applications.

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Active control of geometrically nonlinear transient vibration of composite plates with piezoelectric actuators

Cited by 88 publications

References 15 publications

Coupled finite element for the nonlinear dynamic response of active piezoelectric plates under thermoelectromechanical loads

Coupled finite element for the nonlinear dynamic response of active piezoelectric plates under thermoelectromechanical loads

Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS

Piezoelectric materials selection for sensor applications using finite element and multiple attribute decision-making approaches

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