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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.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.Improved shunt damping with two negative capacitances: an efficient alternative to resonant shunt
http://hdl.handle.net/10985/11321
Improved shunt damping with two negative capacitances: an efficient alternative to resonant shunt
BERARDENGO, Marta; THOMAS, Olivier; GIRAUD-AUDINE, Christophe; MANZONI, Stefano
This paper deals with piezoelectric shunt damping enhanced with negative capacitances. A novel electrical circuit layout is addressed, based on the use of two negative capacitances. It is shown that the shunt performances, in terms of vibration reduction and stability margins, are increased as compared with the classical single negative capacitance layouts. Then, the article focuses on the comparison of a simple resistive shunt, enhanced by a pair of negative capacitances, with a classical resonant shunt. It is shown that the newly proposed enhanced resistive shunt can show equivalent performances in terms of vibration attenuation than the resonant shunt, with at the same time an increased robustness to frequency detuning, in the case of mono-modal damping. The broadband control capability of the resistive shunt coupled to the new negative capacitance layout is also evidenced. The main part of the work is analytical, and then the model is validated by an extensive experimental campaign at the end of the paper.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/113212016-01-01T00:00:00ZBERARDENGO, MartaTHOMAS, OlivierGIRAUD-AUDINE, ChristopheMANZONI, StefanoThis paper deals with piezoelectric shunt damping enhanced with negative capacitances. A novel electrical circuit layout is addressed, based on the use of two negative capacitances. It is shown that the shunt performances, in terms of vibration reduction and stability margins, are increased as compared with the classical single negative capacitance layouts. Then, the article focuses on the comparison of a simple resistive shunt, enhanced by a pair of negative capacitances, with a classical resonant shunt. It is shown that the newly proposed enhanced resistive shunt can show equivalent performances in terms of vibration attenuation than the resonant shunt, with at the same time an increased robustness to frequency detuning, in the case of mono-modal damping. The broadband control capability of the resistive shunt coupled to the new negative capacitance layout is also evidenced. The main part of the work is analytical, and then the model is validated by an extensive experimental campaign at the end of the paper.Wafer-scale fabrication of self-actuated piezoelectric nanoelectromechanical resonators based on lead zirconate titanate (PZT)
http://hdl.handle.net/10985/15355
Wafer-scale fabrication of self-actuated piezoelectric nanoelectromechanical resonators based on lead zirconate titanate (PZT)
DEZEST, D; THOMAS, Olivier; MATHIEU, F; MAZENQ, L; SOYER, C; COSTECALDE, J; REMIENS, D; DEÜ, J F; NICU, L
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/10985/153552015-01-01T00:00:00ZDEZEST, DTHOMAS, OlivierMATHIEU, FMAZENQ, LSOYER, CCOSTECALDE, JREMIENS, DDEÜ, J FNICU, LIn 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.A Novel Method for Accelerating the Analysis of Nonlinear Behaviour of Power Grids using Normal Form Technique
http://hdl.handle.net/10985/18014
A Novel Method for Accelerating the Analysis of Nonlinear Behaviour of Power Grids using Normal Form Technique
UGWUANYI, Nnaemeka Sunday; KESTELYN, Xavier; THOMAS, Olivier; MARINESCU, Bogdan
Today's power systems are strongly nonlinear and are becoming more complex with the large penetration of power-electronics interfaced generators. Conventional Linear Modal Analysis does not adequately study such a system with complex nonlinear behavior. Inclusion of higher-order terms in small-signal (modal) analysis associated with the Normal Form theory proposes a nonlinear modal analysis as an efficient way to improve the analysis. However, heavy computations involved make Normal Form method tedious, and impracticable for large power system application. In this paper, we present an efficient and speedy approach for obtaining the required nonlinear coefficients of the nonlinear equations modelling of a power system, without actually going through all the usual high order differentiation involved in Taylor series expansion. The method uses eigenvectors to excite the system modes independently which lead to formulation of linear equations whose solution gives the needed coefficients. The proposed method is demonstrated on the conventional IEEE 9-bus system and 68-bus New England/New York system.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/180142019-01-01T00:00:00ZUGWUANYI, Nnaemeka SundayKESTELYN, XavierTHOMAS, OlivierMARINESCU, BogdanToday's power systems are strongly nonlinear and are becoming more complex with the large penetration of power-electronics interfaced generators. Conventional Linear Modal Analysis does not adequately study such a system with complex nonlinear behavior. Inclusion of higher-order terms in small-signal (modal) analysis associated with the Normal Form theory proposes a nonlinear modal analysis as an efficient way to improve the analysis. However, heavy computations involved make Normal Form method tedious, and impracticable for large power system application. In this paper, we present an efficient and speedy approach for obtaining the required nonlinear coefficients of the nonlinear equations modelling of a power system, without actually going through all the usual high order differentiation involved in Taylor series expansion. The method uses eigenvectors to excite the system modes independently which lead to formulation of linear equations whose solution gives the needed coefficients. The proposed method is demonstrated on the conventional IEEE 9-bus system and 68-bus New England/New York system.Power System Nonlinear Modal Analysis Using Computationally Reduced Normal Form Method
http://hdl.handle.net/10985/18337
Power System Nonlinear Modal Analysis Using Computationally Reduced Normal Form Method
UGWUANYI, Nnaemeka Sunday; KESTELYN, Xavier; MARINESCU, Bogdan; THOMAS, Olivier
Increasing nonlinearity in today’s grid challenges the conventional small-signal (modal) analysis (SSA) tools. For instance, the interactions among modes, which are not captured by SSA, may play significant roles in a stressed power system. Consequently, alternative nonlinear modal analysis tools, notably Normal Form (NF) and Modal Series (MS) methods are being explored. However, they are computation-intensive due to numerous polynomial coefficients required. This paper proposes a fast NF technique for power system modal interaction investigation, which uses characteristics of system modes to carefully select relevant terms to be considered in the analysis. The Coefficients related to these terms are selectively computed and the resulting approximate model is computationally reduced compared to the one in which all the coefficients are computed. This leads to a very rapid nonlinear modal analysis of the power systems. The reduced model is used to study interactions of modes in a two-area power system where the tested scenarios give same results as the full model, with about 70% reduction in computation time.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/183372020-01-01T00:00:00ZUGWUANYI, Nnaemeka SundayKESTELYN, XavierMARINESCU, BogdanTHOMAS, OlivierIncreasing nonlinearity in today’s grid challenges the conventional small-signal (modal) analysis (SSA) tools. For instance, the interactions among modes, which are not captured by SSA, may play significant roles in a stressed power system. Consequently, alternative nonlinear modal analysis tools, notably Normal Form (NF) and Modal Series (MS) methods are being explored. However, they are computation-intensive due to numerous polynomial coefficients required. This paper proposes a fast NF technique for power system modal interaction investigation, which uses characteristics of system modes to carefully select relevant terms to be considered in the analysis. The Coefficients related to these terms are selectively computed and the resulting approximate model is computationally reduced compared to the one in which all the coefficients are computed. This leads to a very rapid nonlinear modal analysis of the power systems. The reduced model is used to study interactions of modes in a two-area power system where the tested scenarios give same results as the full model, with about 70% reduction in computation time.Optimization of length and thickness of smart transduction layers on beam structures for control and M/NEMS applications
http://hdl.handle.net/10985/10257
Optimization of length and thickness of smart transduction layers on beam structures for control and M/NEMS applications
THOMAS, Olivier; LEGRAND, Bernard; FUINEL, Cécile
This work addresses the optimization of the geometry of smart sensors and actuators on cantilever beams. Three transduction principles are studied and compared in term of efficiency: piezoelectric, electrostatic and dielectric. For the piezoelectric transduction, an active layer of a shorter length than the one of the beam is added on its surfaces. For the electrostatic transduction, the beam is made of a conducting material and it is faced with a fixed electrode at a distance called the gap. This architecture is widely used for M/NEMS (Micro/Nano ElectroMechanical Systems). The last transduction principle, new and promising, is based on the use of dielectric layers on the beam surface. In this case, the excitation is based on electrostatic forces between the charged electrodes, causing transverse deformation of the dielectric film and bending of the multilayer structure; the detection of the vibration is capacitive, based on the fluctuation of the capacitance due to the deformation of the dielectric film. This work presents the optimization of the length and the thickness of the piezoelectric/dielectric layers and, for the electrostatic case, the optimization of the length and the gap of the electrostatic cavity. The study is based on an analytic model for a laminated beam and closed-form formula of the optimization parameters (coupling factor, driving efficiency, sensing efficiency) are obtained. The application of those three transduction principles mainly focus on resonating M/NEMS sensors, whereas the case of piezoelectric transduction is also useful for vibration control of macro structures, especially with passive shunt techniques. General results on the comparison of the transduction efficiency, as a function of the device size and of the material properties, are also derived.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/102572015-01-01T00:00:00ZTHOMAS, OlivierLEGRAND, BernardFUINEL, CécileThis work addresses the optimization of the geometry of smart sensors and actuators on cantilever beams. Three transduction principles are studied and compared in term of efficiency: piezoelectric, electrostatic and dielectric. For the piezoelectric transduction, an active layer of a shorter length than the one of the beam is added on its surfaces. For the electrostatic transduction, the beam is made of a conducting material and it is faced with a fixed electrode at a distance called the gap. This architecture is widely used for M/NEMS (Micro/Nano ElectroMechanical Systems). The last transduction principle, new and promising, is based on the use of dielectric layers on the beam surface. In this case, the excitation is based on electrostatic forces between the charged electrodes, causing transverse deformation of the dielectric film and bending of the multilayer structure; the detection of the vibration is capacitive, based on the fluctuation of the capacitance due to the deformation of the dielectric film. This work presents the optimization of the length and the thickness of the piezoelectric/dielectric layers and, for the electrostatic case, the optimization of the length and the gap of the electrostatic cavity. The study is based on an analytic model for a laminated beam and closed-form formula of the optimization parameters (coupling factor, driving efficiency, sensing efficiency) are obtained. The application of those three transduction principles mainly focus on resonating M/NEMS sensors, whereas the case of piezoelectric transduction is also useful for vibration control of macro structures, especially with passive shunt techniques. General results on the comparison of the transduction efficiency, as a function of the device size and of the material properties, are also derived.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.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.Efficient parametric amplification in micro-resonators with integrated piezoelectric actuation and sensing capabilities
http://hdl.handle.net/10985/8827
Efficient parametric amplification in micro-resonators with integrated piezoelectric actuation and sensing capabilities
THOMAS, Olivier; FABRICE, Mathieu; MANSFIELD, W.; HUANG, C.; TROLIER MCKINSTRY, Susan; NICU, Liviu
We report, in this work, on unprecedented levels of parametric amplification in microelectromechanical resonators, operated in air, with integrated piezoelectric actuation and sensing capabilities. The method relies on an analytical/numerical understanding of the influence of geometrical nonlinearities inherent to the bridge-like configuration of the resonators. We provide analytical formulae to predict the performances of the parametric amplifier below the nonlinearity threshold, in terms of gain and quality factor (Q) enhancement. The analysis explains how to overcome this nonlinearity threshold by controlling the drive signals. It predicts that in theory, any Q-factor enhancement can be achieved. Experimental validation demonstrates a Q-factor enhancement by up to a factor 14 in air.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/88272013-01-01T00:00:00ZTHOMAS, OlivierFABRICE, MathieuMANSFIELD, W.HUANG, C.TROLIER MCKINSTRY, SusanNICU, LiviuWe report, in this work, on unprecedented levels of parametric amplification in microelectromechanical resonators, operated in air, with integrated piezoelectric actuation and sensing capabilities. The method relies on an analytical/numerical understanding of the influence of geometrical nonlinearities inherent to the bridge-like configuration of the resonators. We provide analytical formulae to predict the performances of the parametric amplifier below the nonlinearity threshold, in terms of gain and quality factor (Q) enhancement. The analysis explains how to overcome this nonlinearity threshold by controlling the drive signals. It predicts that in theory, any Q-factor enhancement can be achieved. Experimental validation demonstrates a Q-factor enhancement by up to a factor 14 in air.