&lt;title&gt;Nonlinear finite element modeling of vibration control of composite piezolaminated composite plates and shells&lt;/title&gt;

Lentzen, S.; Schmidt, Rüdiger

doi:10.1117/12.599586

Cited by 5 publications

(6 citation statements)

References 29 publications

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“…Since the eigenshapes in the geometrically nonlinear configuration are not significantly different from those of the initial configuration, one could conclude that the efficiency of the control does not noticeably reduce when the sensor weights obtained from the linear eigenmode analysis are deployed. However, as has been shown in [26,28,38], the modal sensing principle as used in this work rapidly loses its accuracy when the amplitudes of vibration become even slightly larger. A FFT analysis is performed on the resulting modal signal for the third mode and signal is displayed in the lower graph of figure 12.…”

Section: Clamped Semicircular Shellmentioning

confidence: 86%

“…Recently Mukherjee and Chaudhuri [31] 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 [26][27][28][29] 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. Batra et al [4,5] dealt with shape and vibration control of plates at finite deformations, also taking into account nonlinear constitutive equations for piezoelectric patches.…”

Section: Introductionmentioning

confidence: 99%

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Geometrically nonlinear finite element simulation of smart piezolaminated plates and shells

Lentzen

Kl̵osowski

Schmidt

2007

Smart Mater. Struct.

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In this work a geometrically nonlinear finite shell element is presented, incorporating piezoelectric layers. The finite element is implemented in a total Lagrangian approach, which requires special attention to be given to the proper definition of the mechanical and electrical quantities. The strain–displacement relations are based on the assumption of small strains and moderate rotations. The transverse displacement field and the transverse electric potential are assumed to vary linearly through the thickness. With the presented finite element, static as well as dynamic examples are calculated. The differences between the results obtained with linear and nonlinear theory are emphasized.

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Section: Clamped Semicircular Shellmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear finite element simulation of smart piezolaminated plates and shells

Lentzen

Kl̵osowski

Schmidt

2007

Smart Mater. Struct.

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“…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%

“…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. Large rotations were analyzed by Zhang and Schmidt [59].…”

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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“…Gao and Shen [27] derived an incremental finite element model to demonstrate that the piezoelectric actuator can introduce significant damping and suppress geometrically nonlinear transient vibrations of composite plates. Lentzen and Schmidt [28,29] also developed finite element models to carry out geometrically nonlinear static and dynamic analyses of composite structures integrated with piezoelectric layer as actuators and sensors. Most recently, Kulkarni and Bajoria [30] presented the geometrically nonlinear analysis of smart thin and sandwich plates.…”

Section: Introductionmentioning

confidence: 99%

Geometrically Nonlinear Finite Element Analysis of Composite Plates Integrated with the Patches of Piezoelectric Fiber-reinforced Composite

Shivakumar

Ray

2008

Journal of Reinforced Plastics and Composites

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Geometrically nonlinear static analysis of laminated smart composite plates integrated with the patches of piezoelectric fiber-reinforced composite (PFRC) material acting as the distributed actuators has been carried out by a generalized energy based finite element model. The Von Karman type nonlinear strain displacement relations and a simple first-order shear deformation theory are used for deriving this coupled electromechanical finite element model. Eight-noded isoparametric serendipity elements are used for discretizing the overall plates. The nonlinear finite element equilibrium equations are solved by Picard's direct iteration method under relaxation. The performance of the PFRC patches has been investigated for both symmetric and antisymmetric cross-ply and antisymmetric angle-ply laminated composite plate substrates with different boundary conditions. Particular emphasis has been placed on investigating the effect of variation of piezoelectric fiber orientation on the actuating capability of the PFRC patches for counteracting the nonlinear deformations of the smart composite plates. The results suggest the potential use of the patches of PFRC material for distributed control of nonlinear deformations of smart composite structures.

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<title>Nonlinear finite element modeling of vibration control of composite piezolaminated composite plates and shells</title>

Cited by 5 publications

References 29 publications

Geometrically nonlinear finite element simulation of smart piezolaminated plates and shells

Geometrically nonlinear finite element simulation of smart piezolaminated plates and shells

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

Geometrically Nonlinear Finite Element Analysis of Composite Plates Integrated with the Patches of Piezoelectric Fiber-reinforced Composite

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