Nonlinear dynamic response of piezolaminated smart beams

Mukherjee, Abhijit; Chaudhuri, Arup Saha

doi:10.1016/j.compstruc.2004.06.008

Cited by 39 publications

(17 citation statements)

References 15 publications

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“…Conversely, Figure 2 illustrates the tip vibration of the beam subject to a tensile axial load and shows an amplitude reduction with a simultaneous vibration period reduction due to stiffening effects produced by the axial tensile load. Finally, the results are in excellent agreement with those reported by Mukherjee and Chaudhuri [2005] who used a beam finite element based on uncoupled laminate theory.…”

Section: Validation Casessupporting

confidence: 81%

“…Yi et al [2000] applied solid elements to perform geometrically nonlinear analysis of surface bonded piezoelectric sensor wafers on plates and shells. Mukherjee and Chaudhuri [2005] developed a finite element for piezolaminated beams using an uncoupled approach for the prediction of sensory voltage in polyvinylidene fluoride (PVDF) bimorph cantilever beams vibrating at large amplitudes. Lentzen et al [2007] worked on the control of the nonlinear vibration of piezoelectric beams under transverse load.…”

Section: Introductionmentioning

confidence: 99%

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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: Validation Casessupporting

confidence: 81%

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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“…Yi et al [53] used solid elements for geometrically nonlinear analysis of the sensor voltage output of surface-bonded piezoelectric patches on beams, plates, and shells. Recently, Mukherjee and Chaudhuri [54] have analyzed the generation of sensed voltage due to nonlinear vibrations of a PVDF bimorph cantilever beam by adopting the von Kármán nonlinearity in the framework of first-order shear deformation theory. The sensor voltage output of surface-bonded piezoelectric patches on beams, plates, and shells has been analyzed in the framework of a nonlinear moderate rotation first-order shear deformation theory in recent papers (Lentzen and Schmidt [55][56][57][58], Rao et al [60]).…”

Section: Introductionmentioning

confidence: 99%

“…Tzou and Zhou [66,67], Zhou and Tzou [68] studied the active control of nonlinear piezoelectric circular plates and shells with von Kármán-type geometric nonlinearity. Recently, Mukherjee and Chaudhuri [54] adopted the von Kármán nonlinearity in the framework of first-order shear deformation theory for nonlinear vibration control of a PVDF bimorph cantilever beam. Lentzen and Schmidt [55][56][57][58] developed a finite element code for the simulation of nonlinear vibration control of smart isotropic or composite laminated beams, plates, and shells with integrated piezoelectric actuator and sensor layers based on a moderate rotation first-order shear deformation model.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

Chróścielewski

Schmidt

Eremeyev

2018

Continuum Mech. Thermodyn.

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This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

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Nonlinear dynamic response of piezolaminated smart beams

Cited by 39 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

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

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