Experimental analysis of nonlinear resonances in piezoelectric plates with geometric nonlinearities

Givois, Arthur; Giraud-Audine, Christophe; Deü, Jean-François; Thomas, Olivier

doi:10.1007/s11071-020-05997-6

Cited by 12 publications

(7 citation statements)

References 65 publications

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“…Important consequences are in the field of identification methods, where minimal nonlinear models can be used reliably, see, e.g. circular plates with 1:1 internal resonances [68,70,272], shallow shells with 1:1:2 and 1:2:2:4 internal resonances [106,184,274], MEMS structure with 1:2 and 1:3 resonance [42,71], and the identification of the hardening/softening behaviour of particular modes of a structure [45].…”

Section: Applicationsmentioning

confidence: 99%

“…In this realm, the following directions should be investigated soon as direct applications of the general method. First of all, applications to different physical problems, including different types of nonlinear forces, should be investigated, as for example nonlinear damping laws [5,6,37], coupling with other physical forces such as piezoelectric couplings [68,138,250], piezoelectric material nonlinearities [62,139,299], non-local models for nanostructures [238,239], often used in energy-harvesting problems, electrostatic forces in MEMS dynamics [319], centrifugal and Coriolis effects in rotating systems [44,267] with applications to blades [79,224,226,271], large strain elastic nonlinear constitutive laws [187], fluid-structure interaction [107,165] and coupling with nonlinear aeroelastic forces [48]; or thermal effects [99,219], to cite a few of the most obvious directions where the general reduction strategy could be easily extended. Extensions to structures with symmetries, in order to get more quantitative informations and highlight the link with mode localization, could be also used with such tools [65,291,308,309].…”

Section: Open Problems and Future Directionsmentioning

confidence: 99%

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Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

2021

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This paper aims at reviewing nonlinear methods for model order reduction in structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear-based techniques by their use of a nonlinear mapping instead of adding new vectors to enlarge the projection basis. Invariant manifolds have been first introduced in vibration theory within the context of nonlinear normal modes and have been initially computed from the modal basis, using either a graph representation or a normal form approach to compute mappings and reduced dynamics. These developments are first recalled following a historical perspective, where the main applications were first oriented toward structural models that can be expressed thanks to partial differential equations. They are then replaced in the more general context of the parametrisation of invariant manifold that allows unifying the approaches. Then, the specific case of structures dis-C. Touzé (B)

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Section: Applicationsmentioning

confidence: 99%

Section: Open Problems and Future Directionsmentioning

confidence: 99%

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

2021

Self Cite

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“…Important consequences are in the field of identification methods, where minimal nonlinear models can be used reliably, see e.g. circular plates with 1:1 internal resonances [66,68,273], shallow shells with 1:1:2 and 1:2:2:4 internal resonances [104,185,275], MEMS structure with 1:2 and 1:3 resonance [42,69], and the identification of the hardening/softening behaviour of particular modes of a structure [45].…”

Section: Applicationsmentioning

confidence: 99%

“…In this realm, the following directions should be investigated soon as direct applications of the general method. First of all, applications to different physical problems, including different types of nonlinear forces, should be investigated, as for example nonlinear damping laws [5,6,37], coupling with other physical forces such as piezoelectric couplings [66,137,251], piezoelectric material nonlinearities [60,138,299], non-local models for nanostructures [239,240], often used in energy-harvesting problems, electrostatic forces in MEMS dynamics [319], centrifugal and Coriolis effects in rotating systems [44,268] with applications to blades [77,225,227,272], large strain elastic nonlinear constitutive laws [188], fluid-structure interaction [105,166] and coupling with nonlinear aeroelastic forces [46]; or thermal effects [97,220], to cite a few of the most obvious directions where the general reduction strategy could be easily extended. Extensions to structures with symmetries, in order to get more quantitative informations and highlight the link with mode localization could be also used with such tools [63,292,308,309].…”

Section: Open Problems and Future Directionsmentioning

confidence: 99%

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Touzé,

Vizzaccaro,

Thomas

2021

Preprint

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This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based techniques by their use of a nonlinear mapping instead of adding new vectors to enlarge the projection basis. Invariant manifolds have been first introduced in vibration theory within the context of nonlinear normal modes (NNMs) and have been initially computed from the modal basis, using either a graph representation or a normal form approach to compute mappings and reduced dynamics. These developments are first recalled following a historical perspective, where the main applications were first oriented toward structural models that can be expressed thanks to partial differential equations (PDE). They are then replaced in the more general context of the parametrisation of invariant manifold that allows unifying the approaches. Then the specific case of structures discretized with the finite element method is addressed. Implicit condensation, giving rise to a projection onto a stress manifold, and modal derivatives, used in the framework of the quadratic manifold, are first reviewed. Finally, recent developments allowing direct computation of reduced-order models (ROMs) relying on invariant manifolds theory are detailed. Applicative examples are shown and the extension of the methods to deal with further complications are reviewed. Finally, open problems and future directions are highlighted.

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“…The present work aims at filling the lack of knowledge regarding the characterization of the nonlinear dynamic features of roller battery systems and to investigate the effects of the periodic excitations induced by the moving cable that may give rise to resonance phenomena and nonlinear modal interactions. These phenomena were studied in the past in different mechanical systems, such as cranes [16][17][18][19], tethering [20], pendulum systems [21,22], piezoelectric beams [23,24], and plates [25,26], or, more generally, in slender structures possessing strong geometric nonlinearities [27][28][29]. Such nonlinearities can affect the dynamic response of highly deformable structural elements and can be suitably exploited for practical applications, as it was largely demonstrated in the literature [30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Response of Ropeway Roller Batteries via an Asymptotic Approach

Arena¹

2021

Applied Sciences

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The nonlinear dynamic features of compression roller batteries were investigated together with their nonlinear response to primary resonance excitation and to internal interactions between modes. Starting from a parametric nonlinear model based on a previously developed Lagrangian formulation, asymptotic treatment of the equations of motion was first performed to characterize the nonlinearity of the lowest nonlinear normal modes of the system. They were found to be characterized by a softening nonlinearity associated with the stiffness terms. Subsequently, a direct time integration of the equations of motion was performed to compute the frequency response curves (FRCs) when the system is subjected to direct harmonic excitations causing the primary resonance of the lowest skew-symmetric mode shape. The method of multiple scales was then employed to study the bifurcation behavior and deliver closed-form expressions of the FRCs and of the loci of the fold bifurcation points, which provide the stability regions of the system. Furthermore, conditions for the onset of internal resonances between the lowest roller battery modes were found, and a 2:1 resonance between the third and first modes of the system was investigated in the case of harmonic excitation having a frequency close to the first mode and the third mode, respectively.

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Experimental analysis of nonlinear resonances in piezoelectric plates with geometric nonlinearities

Cited by 12 publications

References 65 publications

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Nonlinear Dynamic Response of Ropeway Roller Batteries via an Asymptotic Approach

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