Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS
dc.contributor.author
hal.structure.identifier | LAZARUS, Arnaud
|
dc.contributor.author
hal.structure.identifier | THOMAS, Olivier
|
dc.contributor.author
hal.structure.identifier | DEÜ, Jean-François
|
dc.date.accessioned | 2014 |
dc.date.available | 2014 |
dc.date.issued | 2012 |
dc.date.submitted | 2014 |
dc.identifier.issn | 0168-874X |
dc.identifier.uri | http://hdl.handle.net/10985/8955 |
dc.description.abstract | This 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 Kármán 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 Kármán 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. |
dc.description.sponsorship | This research is part of the NEMSPIEZO project, under funds from the French National Research Agency (Project ANR-08-NAN O-015-04), for which the authors are grateful. |
dc.language.iso | en |
dc.publisher | Elsevier |
dc.rights | Post-print |
dc.subject | Continuation methods |
dc.subject | Nanoelectromechanical systems |
dc.subject | Nonlinear vibrations |
dc.subject | Piezoelectric materials |
dc.subject | Reduced order models |
dc.title | Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS |
dc.identifier.doi | 10.1016/j.finel.2011.08.019 |
dc.typdoc | Article dans une revue avec comité de lecture |
dc.localisation | Centre de Lille |
dc.subject.hal | Physique: Instrumentations et Détecteurs |
dc.subject.hal | Sciences de l'ingénieur: Mécanique |
dc.subject.hal | Sciences de l'ingénieur: Mécanique: Matériaux et structures en mécanique |
dc.subject.hal | Sciences de l'ingénieur: Mécanique: Mécanique des solides |
dc.subject.hal | Sciences de l'ingénieur: Mécanique: Mécanique des structures |
dc.subject.hal | Sciences de l'ingénieur: Mécanique: Vibrations |
dc.subject.hal | Sciences de l'ingénieur: Micro et nanotechnologies/Microélectronique |
ensam.audience | Internationale |
ensam.page | 35-51 |
ensam.journal | Finite Elements in Analysis and Design |
ensam.volume | 49 |
ensam.issue | 1 |
hal.identifier | hal-01084700 |
hal.version | 1 |
hal.submission.permitted | updateMetadata |
hal.status | accept |