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http://hdl.handle.net/10985/24164
Extreme nonlinear dynamics of cantilever beams: effect of gravity and slenderness on the nonlinear modes
DEBEURRE, Marielle; GROLET, Aurélien; THOMAS, Olivier
In this paper, the effect of gravity on the nonlinear extreme amplitude vibrations of a slender, vertically-oriented cantilever beam is investigated. The extreme nonlinear vibrations are modeled using a finite element discretization of the geometrically exact beam model solved in the frequency domain through a combination of harmonic balance and a continuation method for periodic solutions. The geometrically exact model is ideal for dynamic simulations at extreme amplitudes as there is no limitation on the rotation of the cross-sections due to the terms governing the rotation being kept exact. It is shown that the very large amplitude vibrations of dimensionless beam structures depend principally on two parameters, a geometrical parameter and a gravity parameter. By varying these two parameters, the effect of gravity in either a standing or hanging configuration on the natural (linear) modes as well as on the nonlinear modes in extreme amplitude vibration is studied. It is shown that gravity, in the case of a standing cantilever, is responsible for a linear softening behavior and a nonlinear hardening behavior, particularly pronounced on the first bending mode. These behaviors are reversed for a hanging cantilever.
Thu, 15 Jun 2023 00:00:00 GMThttp://hdl.handle.net/10985/241642023-06-15T00:00:00ZDEBEURRE, MarielleGROLET, AurélienTHOMAS, OlivierIn this paper, the effect of gravity on the nonlinear extreme amplitude vibrations of a slender, vertically-oriented cantilever beam is investigated. The extreme nonlinear vibrations are modeled using a finite element discretization of the geometrically exact beam model solved in the frequency domain through a combination of harmonic balance and a continuation method for periodic solutions. The geometrically exact model is ideal for dynamic simulations at extreme amplitudes as there is no limitation on the rotation of the cross-sections due to the terms governing the rotation being kept exact. It is shown that the very large amplitude vibrations of dimensionless beam structures depend principally on two parameters, a geometrical parameter and a gravity parameter. By varying these two parameters, the effect of gravity in either a standing or hanging configuration on the natural (linear) modes as well as on the nonlinear modes in extreme amplitude vibration is studied. It is shown that gravity, in the case of a standing cantilever, is responsible for a linear softening behavior and a nonlinear hardening behavior, particularly pronounced on the first bending mode. These behaviors are reversed for a hanging cantilever.Finite 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.Dynamic stability of centrifugal pendulum vibration absorbers allowing a rotational mobility
http://hdl.handle.net/10985/22538
Dynamic stability of centrifugal pendulum vibration absorbers allowing a rotational mobility
MAHE, V.; RENAULT, Alexandre; GROLET, Aurélien; THOMAS, Olivier; MAHE, Hervé
Centrifugal pendulum vibration absorbers (CPVA) are used in the automobile industry to reduce the vibrations of the transmission system. These passive devices are made of several masses oscillating along a given trajectory relative to the rotor. In this paper, the dynamic stability of a new class of CPVA is investigated. The particularity of this new class is that masses now admit a
significant rotation motion relative to the rotor, in addition to the traditional translation motion. The efficiency of such devices is optimal for a perfect synchronous motion of the oscillating masses. However, masses unison can be broken for the benefit of energy localisation on a given absorber, leading to a loss of mitigation performances. To assess the stability of such devices,
a dynamical model based on an analytic perturbation method is established. The aim of this model is to predict analytically localisation and jumps of the response. The validity of the model is confirmed through a comparison with both a numerical resolution of the system’s dynamics and an experimental study.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10985/225382022-01-01T00:00:00ZMAHE, V.RENAULT, AlexandreGROLET, AurélienTHOMAS, OlivierMAHE, HervéCentrifugal pendulum vibration absorbers (CPVA) are used in the automobile industry to reduce the vibrations of the transmission system. These passive devices are made of several masses oscillating along a given trajectory relative to the rotor. In this paper, the dynamic stability of a new class of CPVA is investigated. The particularity of this new class is that masses now admit a
significant rotation motion relative to the rotor, in addition to the traditional translation motion. The efficiency of such devices is optimal for a perfect synchronous motion of the oscillating masses. However, masses unison can be broken for the benefit of energy localisation on a given absorber, leading to a loss of mitigation performances. To assess the stability of such devices,
a dynamical model based on an analytic perturbation method is established. The aim of this model is to predict analytically localisation and jumps of the response. The validity of the model is confirmed through a comparison with both a numerical resolution of the system’s dynamics and an experimental study.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.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.Singular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditions
http://hdl.handle.net/10985/8953
Singular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditions
NEUKIRCH, Sébastien; GORIELY, Alain; THOMAS, Olivier
In-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible planar Kirchhoff elastic rod under large displacements and rotations. Equilibrium configurations and vibrations around these configurations are computed analytically in the incipient post-buckling regime. Of particular interest is the variation of the first mode frequency as the load is increased through the buckling threshold. The loading type is found to have a crucial importance as the first mode frequency is shown to behave singularly in the zero thickness limit in the case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/89532014-01-01T00:00:00ZNEUKIRCH, SébastienGORIELY, AlainTHOMAS, OlivierIn-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible planar Kirchhoff elastic rod under large displacements and rotations. Equilibrium configurations and vibrations around these configurations are computed analytically in the incipient post-buckling regime. Of particular interest is the variation of the first mode frequency as the load is increased through the buckling threshold. The loading type is found to have a crucial importance as the first mode frequency is shown to behave singularly in the zero thickness limit in the case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load.Piezoelectric amplifiers with integrated actuation and sensing capabilities
http://hdl.handle.net/10985/10105
Piezoelectric amplifiers with integrated actuation and sensing capabilities
THOMAS, Olivier; MATHIEU, Fabrice; MANSFIELD, W.; HUANG, C.; TROLIER MCKINSTRY, Susan; NICU, Liviu
We report in this work on unprecedented levels of parametric amplification in microelectromechanical systems (MEMS) resonators with integrated piezoelectric actuation and sensing capabilities operated in air. The method presented here relies on accurate analytical modeling taking into account the geometrical nonlinearities inherent to the bridge-like configuration of the resonators used. The model provides, for the first time, precise analytical formula of the quality factor (Q) enhancement depending on the resonant mode examined. Experimental validations were conducted for resonant modes exhibiting, respectively, hard and soft-spring effects when driven in the nonlinear regime; Q amplification by a factor up to 14 has been obtained in air.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/101052013-01-01T00:00:00ZTHOMAS, OlivierMATHIEU, FabriceMANSFIELD, W.HUANG, C.TROLIER MCKINSTRY, SusanNICU, LiviuWe report in this work on unprecedented levels of parametric amplification in microelectromechanical systems (MEMS) resonators with integrated piezoelectric actuation and sensing capabilities operated in air. The method presented here relies on accurate analytical modeling taking into account the geometrical nonlinearities inherent to the bridge-like configuration of the resonators used. The model provides, for the first time, precise analytical formula of the quality factor (Q) enhancement depending on the resonant mode examined. Experimental validations were conducted for resonant modes exhibiting, respectively, hard and soft-spring effects when driven in the nonlinear regime; Q amplification by a factor up to 14 has been obtained in air.Extreme nonlinear dynamics of cantilever beams: effect of gravity and slenderness on the nonlinear modes
http://hdl.handle.net/10985/24781
Extreme nonlinear dynamics of cantilever beams: effect of gravity and slenderness on the nonlinear modes
DEBEURRE, Marielle; GROLET, Aurélien; THOMAS, Olivier
In this paper, the effect of gravity on the nonlinear extreme amplitude vibrations of a slender, vertically oriented cantilever beam is investigated. The extreme nonlinear vibrations aremodeled using a finite element discretization of the geometrically exact beam
model solved in the frequency domain through a combination of harmonic balance and a continuation method for periodic solutions.The geometrically exact model is ideal for dynamic simulations at extreme amplitudes as there is no limitation on the rotation of the cross sections due to the terms governing the rotation being kept exact. It is shown that the very large amplitude vibrations of dimensionless beam structures depend principally on two parameters, a geometrical parameter and a gravity
parameter. By varying these two parameters, the effect of gravity in either a standing or hanging configuration
on the natural (linear)modes as well as on the nonlinear modes in extreme amplitude vibration is studied. It is shown that gravity, in the case of a standing cantilever, is responsible for a linear softening behavior and a nonlinear hardening behavior, particularly pronounced on the first bending mode. These behaviors are reversed for a hanging cantilever.
Thu, 01 Jun 2023 00:00:00 GMThttp://hdl.handle.net/10985/247812023-06-01T00:00:00ZDEBEURRE, MarielleGROLET, AurélienTHOMAS, OlivierIn this paper, the effect of gravity on the nonlinear extreme amplitude vibrations of a slender, vertically oriented cantilever beam is investigated. The extreme nonlinear vibrations aremodeled using a finite element discretization of the geometrically exact beam
model solved in the frequency domain through a combination of harmonic balance and a continuation method for periodic solutions.The geometrically exact model is ideal for dynamic simulations at extreme amplitudes as there is no limitation on the rotation of the cross sections due to the terms governing the rotation being kept exact. It is shown that the very large amplitude vibrations of dimensionless beam structures depend principally on two parameters, a geometrical parameter and a gravity
parameter. By varying these two parameters, the effect of gravity in either a standing or hanging configuration
on the natural (linear)modes as well as on the nonlinear modes in extreme amplitude vibration is studied. It is shown that gravity, in the case of a standing cantilever, is responsible for a linear softening behavior and a nonlinear hardening behavior, particularly pronounced on the first bending mode. These behaviors are reversed for a hanging cantilever.Dynamic simulation and optimization of artificial insect-sized flapping wings for a bioinspired kinematics using a two resonant vibration modes combination
http://hdl.handle.net/10985/16792
Dynamic simulation and optimization of artificial insect-sized flapping wings for a bioinspired kinematics using a two resonant vibration modes combination
FAUX, Damien; THOMAS, Olivier; GRONDEL, Sébastien; CATTAN, Éric
This paper addresses the design of the elastic structure of artificial wings to optimize their dynamical behaviour to reproduce insect wings kinematics. Our bioinspired kinematics is based on the original concept of using the resonant properties of the wing structure in order to combine the motion of two vibration modes, a flapping and a twisting mode, in a quadrature phase shift. Oneway of achieving this particular combination is to optimize the geometry and elastic characteristics of the flexible structure such that the two modes are successive in the eigenspectrum and close in frequency. This paper first proposes a semi-analytical model, based on assembled Euler-Bernoulli beams, to understand, compute and optimize the artificial wing dynamic vibrations. Then, using this model, it is shown that it is possible to obtain several artificial wing structures with a flapping and a twisting mode close in frequency. Finally, experimental validations are performed on micromachined insect-sized prototypes to validate the model and the concept.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/167922019-01-01T00:00:00ZFAUX, DamienTHOMAS, OlivierGRONDEL, SébastienCATTAN, ÉricThis paper addresses the design of the elastic structure of artificial wings to optimize their dynamical behaviour to reproduce insect wings kinematics. Our bioinspired kinematics is based on the original concept of using the resonant properties of the wing structure in order to combine the motion of two vibration modes, a flapping and a twisting mode, in a quadrature phase shift. Oneway of achieving this particular combination is to optimize the geometry and elastic characteristics of the flexible structure such that the two modes are successive in the eigenspectrum and close in frequency. This paper first proposes a semi-analytical model, based on assembled Euler-Bernoulli beams, to understand, compute and optimize the artificial wing dynamic vibrations. Then, using this model, it is shown that it is possible to obtain several artificial wing structures with a flapping and a twisting mode close in frequency. Finally, experimental validations are performed on micromachined insect-sized prototypes to validate the model and the concept.Nonlinear vibrations of steelpans: analysis of mode coupling in view of modal sound synthesis.
http://hdl.handle.net/10985/10115
Nonlinear vibrations of steelpans: analysis of mode coupling in view of modal sound synthesis.
MONTEIL, Mélodie; TOUZÉ, Cyril; THOMAS, Olivier
Steelpans are musical percussions made from steel barrels. During the manufacturing, the metal is stretched and bended, to produce a set of thin shells that are the differents notes of the instrument. In normal playing, each note is struck, and the sound reveals some nonlinear characteristics which give its peculiar tone to the instrument. In this paper, an experimental approach is first presented in order to show the complex dynamics existing in steelpan’s vibrations. Then two models, based on typical modal interactions, are proposed to quantify these nonlinearities. Finally, one of them is observed in free oscillations simulations, in order to compare the internal resonance model to the steelpan vibrations behaviour in normal playing. The aim is to identify the important modes participating in the vibrations in view of building reduced-order models for modal sound synthesis.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/101152013-01-01T00:00:00ZMONTEIL, MélodieTOUZÉ, CyrilTHOMAS, OlivierSteelpans are musical percussions made from steel barrels. During the manufacturing, the metal is stretched and bended, to produce a set of thin shells that are the differents notes of the instrument. In normal playing, each note is struck, and the sound reveals some nonlinear characteristics which give its peculiar tone to the instrument. In this paper, an experimental approach is first presented in order to show the complex dynamics existing in steelpan’s vibrations. Then two models, based on typical modal interactions, are proposed to quantify these nonlinearities. Finally, one of them is observed in free oscillations simulations, in order to compare the internal resonance model to the steelpan vibrations behaviour in normal playing. The aim is to identify the important modes participating in the vibrations in view of building reduced-order models for modal sound synthesis.