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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 24 Sep 2022 19:36:10 GMT2022-09-24T19:36:10ZFinite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS
http://hdl.handle.net/10985/8955
Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS
LAZARUS, Arnaud; THOMAS, Olivier; DEÜ, Jean-François
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/89552012-01-01T00:00:00ZLAZARUS, ArnaudTHOMAS, OlivierDEÜ, Jean-FrançoisThis 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.Non-intrusive reduced order modelling for the dynamics of geometrically nonlinear flat structures using three-dimensional finite elements
http://hdl.handle.net/10985/19598
Non-intrusive reduced order modelling for the dynamics of geometrically nonlinear flat structures using three-dimensional finite elements
VIZZACCARO, Alessandra; GIVOIS, Arthur; LONGOBARDI, Pierluigi; SHEN, Yichang; DEÜ, Jean-François; SALLES, Loïc; TOUZÉ, Cyril; THOMAS, Olivier
Non-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on the static application of prescribed displacements in a finite-element context. We show that a particularly slow convergence of the modal expansion is observed when applying the method with 3D elements, because of nonlinear couplings occurring with very high frequency modes involving 3D thickness deformations. Focusing on the case of flat structures, we first show by computing all the modes of the structure that a converged solution can be exhibited by using either static condensation or normal form theory.We then show that static modal derivatives provide the same solution with fewer calculations. Finally, we propose a modified STEP, where the prescribed displacements are imposed solely on specific degrees of freedom of the structure, and show that this adjustment also provides efficiently a converged solution.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/195982020-01-01T00:00:00ZVIZZACCARO, AlessandraGIVOIS, ArthurLONGOBARDI, PierluigiSHEN, YichangDEÜ, Jean-FrançoisSALLES, LoïcTOUZÉ, CyrilTHOMAS, OlivierNon-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on the static application of prescribed displacements in a finite-element context. We show that a particularly slow convergence of the modal expansion is observed when applying the method with 3D elements, because of nonlinear couplings occurring with very high frequency modes involving 3D thickness deformations. Focusing on the case of flat structures, we first show by computing all the modes of the structure that a converged solution can be exhibited by using either static condensation or normal form theory.We then show that static modal derivatives provide the same solution with fewer calculations. Finally, we propose a modified STEP, where the prescribed displacements are imposed solely on specific degrees of freedom of the structure, and show that this adjustment also provides efficiently a converged solution.Wafer-scale integration of piezoelectric actuation capabilities in nanoelectromechanical systems resonators
http://hdl.handle.net/10985/10119
Wafer-scale integration of piezoelectric actuation capabilities in nanoelectromechanical systems resonators
DEZEST, Denis; MATHIEU, Fabrice; MAZENQ, Laurent; SOYER, Caroline; COSTECALDE, Jean; REMIENS, Denis; THOMAS, Olivier; DEÜ, Jean-François; NICU, Liviu
In this work, we demonstrate the integration of piezoelectric actuation means on arrays of nanocantilevers at the wafer scale. We use lead titanate zirconate (PZT) as piezoelectric material mainly because of its excellent actuation properties even when geometrically constrained at extreme scale
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/101192013-01-01T00:00:00ZDEZEST, DenisMATHIEU, FabriceMAZENQ, LaurentSOYER, CarolineCOSTECALDE, JeanREMIENS, DenisTHOMAS, OlivierDEÜ, Jean-FrançoisNICU, LiviuIn this work, we demonstrate the integration of piezoelectric actuation means on arrays of nanocantilevers at the wafer scale. We use lead titanate zirconate (PZT) as piezoelectric material mainly because of its excellent actuation properties even when geometrically constrained at extreme scaleOn the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models
http://hdl.handle.net/10985/16775
On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models
GIVOIS, Arthur; GROLET, Aurélien; THOMAS, Olivier; DEÜ, Jean-François
This paper presents a general methodology to compute nonlinear frequency responses of flat structures subjected to large amplitude transverse vibrations, within a finite element context. A reduced-order model (ROM)is obtained by an expansion onto the eigenmode basis of the associated linearized problem, including transverse and in-plane modes. The coefficients of the nonlinear terms of the ROM are computed thanks to a non-intrusive method, using any existing nonlinear finite element code. The direct comparison to analytical models of beams and plates proves that a lot of coefficients can be neglected and that the in-plane motion can be condensed to the transverse motion, thus giving generic rules to simplify theROM. Then, a continuation technique, based on an asymptotic numerical method and the harmonic balance method, is used to compute the frequency response in free (nonlinear mode computation) or harmonically forced vibrations. The whole procedure is tested on a straight beam, a clamped circular plate and a free perforated plate for which some nonlinear modes are computed, including internal resonances. The convergence with harmonic numbers and oscillators is investigated. It shows that keeping a few of them is sufficient in a range of displacements corresponding to the order of the structure’s thickness, with a complexity of the simulated nonlinear phenomena that increase very fast with the number of harmonics and oscillators.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/167752019-01-01T00:00:00ZGIVOIS, ArthurGROLET, AurélienTHOMAS, OlivierDEÜ, Jean-FrançoisThis paper presents a general methodology to compute nonlinear frequency responses of flat structures subjected to large amplitude transverse vibrations, within a finite element context. A reduced-order model (ROM)is obtained by an expansion onto the eigenmode basis of the associated linearized problem, including transverse and in-plane modes. The coefficients of the nonlinear terms of the ROM are computed thanks to a non-intrusive method, using any existing nonlinear finite element code. The direct comparison to analytical models of beams and plates proves that a lot of coefficients can be neglected and that the in-plane motion can be condensed to the transverse motion, thus giving generic rules to simplify theROM. Then, a continuation technique, based on an asymptotic numerical method and the harmonic balance method, is used to compute the frequency response in free (nonlinear mode computation) or harmonically forced vibrations. The whole procedure is tested on a straight beam, a clamped circular plate and a free perforated plate for which some nonlinear modes are computed, including internal resonances. The convergence with harmonic numbers and oscillators is investigated. It shows that keeping a few of them is sufficient in a range of displacements corresponding to the order of the structure’s thickness, with a complexity of the simulated nonlinear phenomena that increase very fast with the number of harmonics and oscillators.Performance of piezoelectric shunts for vibration reduction
http://hdl.handle.net/10985/8901
Performance of piezoelectric shunts for vibration reduction
THOMAS, Olivier; DUCARNE, Julien; DEÜ, Jean-François
This work addresses passive reduction of structural vibration by means of shunted piezoelectric patches. The two classical resistive and resonant shunt solutions are considered. The main goal of this paper is to give closed-form solutions to systematically estimate the damping performances of the shunts, in the two cases of free and forced vibrations, whatever the elastic host structure is. Then it is carefully demonstrated that the performance of the shunt, in terms of vibration reduction, depends on only one free parameter: the so-called modal electromechanical coupling factor (MEMCF) of the mechanical vibration mode to which the shunts are tuned. Experiments are proposed and an excellent agreement with the model is obtained, thus validating it.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/89012012-01-01T00:00:00ZTHOMAS, OlivierDUCARNE, JulienDEÜ, Jean-FrançoisThis work addresses passive reduction of structural vibration by means of shunted piezoelectric patches. The two classical resistive and resonant shunt solutions are considered. The main goal of this paper is to give closed-form solutions to systematically estimate the damping performances of the shunts, in the two cases of free and forced vibrations, whatever the elastic host structure is. Then it is carefully demonstrated that the performance of the shunt, in terms of vibration reduction, depends on only one free parameter: the so-called modal electromechanical coupling factor (MEMCF) of the mechanical vibration mode to which the shunts are tuned. Experiments are proposed and an excellent agreement with the model is obtained, thus validating it.Wafer-scale fabrication of self-actuated piezoelectric nanoelectromechanical resonators based on lead zirconate titanate (PZT)
http://hdl.handle.net/10985/9654
Wafer-scale fabrication of self-actuated piezoelectric nanoelectromechanical resonators based on lead zirconate titanate (PZT)
DEZEST, Denis; THOMAS, Olivier; MATHIEU, Fabrice; MAZENQ, Laurent; SOYER, Caroline; COSTECALDE, Jean; REMIENS, Denis; DEÜ, Jean-François; NICU, Liviu
In this paper we report an unprecedented level of integration of self-actuated nanoelectromechanical system (NEMS) resonators based on a 150 nm thick lead zirconate titanate (PZT) thin film at the wafer-scale. A top-down approach combining ultraviolet (UV) lithography with other standard planar processing technologies allows us to achieve high-throughput manufacturing. Multilayer stack cantilevers with different geometries have been implemented with measured fundamental resonant frequencies in the megahertz range and Q-factor values ranging from ~130 in air up to ~900 in a vacuum at room temperature. A refined finite element model taking into account the exact configuration of the piezoelectric stack is proposed and demonstrates the importance of considering the dependence of the beam’s cross-section upon the axial coordinate. We extensively investigate both experimentally and theoretically the transduction efficiency of the implemented piezoelectric layer and report for the first time at this integration level a piezoelectric constant of d31 = 15 fm.V−1. Finally, we discuss the current limitations to achieve piezoelectric detection.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/96542015-01-01T00:00:00ZDEZEST, DenisTHOMAS, OlivierMATHIEU, FabriceMAZENQ, LaurentSOYER, CarolineCOSTECALDE, JeanREMIENS, DenisDEÜ, Jean-FrançoisNICU, LiviuIn this paper we report an unprecedented level of integration of self-actuated nanoelectromechanical system (NEMS) resonators based on a 150 nm thick lead zirconate titanate (PZT) thin film at the wafer-scale. A top-down approach combining ultraviolet (UV) lithography with other standard planar processing technologies allows us to achieve high-throughput manufacturing. Multilayer stack cantilevers with different geometries have been implemented with measured fundamental resonant frequencies in the megahertz range and Q-factor values ranging from ~130 in air up to ~900 in a vacuum at room temperature. A refined finite element model taking into account the exact configuration of the piezoelectric stack is proposed and demonstrates the importance of considering the dependence of the beam’s cross-section upon the axial coordinate. We extensively investigate both experimentally and theoretically the transduction efficiency of the implemented piezoelectric layer and report for the first time at this integration level a piezoelectric constant of d31 = 15 fm.V−1. Finally, we discuss the current limitations to achieve piezoelectric detection.Experimental analysis of nonlinear resonances in piezoelectric plates with geometric nonlinearities
http://hdl.handle.net/10985/22640
Experimental analysis of nonlinear resonances in piezoelectric plates with geometric nonlinearities
GIVOIS, Arthur; GIRAUD-AUDINE, Christophe; DEÜ, Jean-François; THOMAS, Olivier
Piezoelectric devices with integrated actuation and sensing capabilities are often used for the development of electromechanical systems. The present paper addresses experimentally the nonlinear dynamics of a fully integrated circular piezoelectric
thin structure, with piezoelectric patches used for actuationand other for sensing. A phase-locked loop control system is used to measure the resonant periodic response of the system under harmonic forcing, in both its stable and unstable parts. The single-mode response around a symmetric resonance as well as the coupled response around an asymmetric resonance, involving two companion modes in 1:1 internal resonance, is accurately measured. For the latter, a particular location of the patches and additional signal processing is proposed to spatially discriminate the response of each companion mode. In addition to a hardening behavior associated with geometric nonlinearities of the plate, a softening behavior predominant at low actuation amplitudes is observed, resulting from the material piezoelectric nonlinearities.
Thu, 01 Oct 2020 00:00:00 GMThttp://hdl.handle.net/10985/226402020-10-01T00:00:00ZGIVOIS, ArthurGIRAUD-AUDINE, ChristopheDEÜ, Jean-FrançoisTHOMAS, OlivierPiezoelectric devices with integrated actuation and sensing capabilities are often used for the development of electromechanical systems. The present paper addresses experimentally the nonlinear dynamics of a fully integrated circular piezoelectric
thin structure, with piezoelectric patches used for actuationand other for sensing. A phase-locked loop control system is used to measure the resonant periodic response of the system under harmonic forcing, in both its stable and unstable parts. The single-mode response around a symmetric resonance as well as the coupled response around an asymmetric resonance, involving two companion modes in 1:1 internal resonance, is accurately measured. For the latter, a particular location of the patches and additional signal processing is proposed to spatially discriminate the response of each companion mode. In addition to a hardening behavior associated with geometric nonlinearities of the plate, a softening behavior predominant at low actuation amplitudes is observed, resulting from the material piezoelectric nonlinearities.Dynamics of piezoelectric structures with geometric nonlinearities: A non-intrusive reduced order modelling strategy
http://hdl.handle.net/10985/22658
Dynamics of piezoelectric structures with geometric nonlinearities: A non-intrusive reduced order modelling strategy
GIVOIS, Arthur; DEÜ, Jean-François; THOMAS, Olivier
A reduced-order modelling to predictively simulate the dynamics of piezoelectric structures with geometric nonlinearities is proposed in this paper. A formulation of three-dimensional finite element models with global electric variables per piezoelectric patch, and suitable with any commercial finite element code equipped with geometrically nonlinear and piezoelectric capabilities, is proposed. A modal expansion leads to a reduced model where both nonlinear and electromechanical coupling effects are governed by modal coefficients, identified thanks to a non-intrusive procedure relying on the static application of prescribed displacements. Numerical simulations can be efficiently performed on the reduced modal model, thus defining a convenient procedure to study accurately the nonlinear dynamics of any piezoelectric structure. A particular focus is made on the parametric effect resulting from the combination of geometric nonlinearities and piezoelectricity. Reference results are provided in terms of coefficients of the reduced-order model as well as of dynamic responses, computed for different test cases including realistic structures.
Wed, 01 Sep 2021 00:00:00 GMThttp://hdl.handle.net/10985/226582021-09-01T00:00:00ZGIVOIS, ArthurDEÜ, Jean-FrançoisTHOMAS, OlivierA reduced-order modelling to predictively simulate the dynamics of piezoelectric structures with geometric nonlinearities is proposed in this paper. A formulation of three-dimensional finite element models with global electric variables per piezoelectric patch, and suitable with any commercial finite element code equipped with geometrically nonlinear and piezoelectric capabilities, is proposed. A modal expansion leads to a reduced model where both nonlinear and electromechanical coupling effects are governed by modal coefficients, identified thanks to a non-intrusive procedure relying on the static application of prescribed displacements. Numerical simulations can be efficiently performed on the reduced modal model, thus defining a convenient procedure to study accurately the nonlinear dynamics of any piezoelectric structure. A particular focus is made on the parametric effect resulting from the combination of geometric nonlinearities and piezoelectricity. Reference results are provided in terms of coefficients of the reduced-order model as well as of dynamic responses, computed for different test cases including realistic structures.