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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.An upper bound for validity limits of asymptotic analytical approaches based on normal form theory
http://hdl.handle.net/10985/7473
An upper bound for validity limits of asymptotic analytical approaches based on normal form theory
LAMARQUE, Claude-Henri; TOUZÉ, Cyril; THOMAS, Olivier
Perturbation methods are routinely used in all fields of applied mathematics where analytical solutions for nonlinear dynamical systems are searched. Among them, normal form theory provides a reliable method for systematically simplifying dynamical systems via nonlinear change of coordinates, and is also used in a mechanical context to define Nonlinear Normal Modes (NNMs). The main recognized drawback of perturbation methods is the absence of a criterion establishing their range of validity in terms of amplitude. In this paper, we propose a method to obtain upper bounds for amplitudes of changes of variables in normal form transformations. The criterion is tested on simple mechanical systems with one and two degrees-of-freedom, and for complex as well as real normal form. Its behavior with increasing order in the normal transform is established, and comparisons are drawn between exact solutions and normal form computations for increasing levels of amplitudes. The results clearly establish that the criterion gives an upper bound for validity limit of normal transforms.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/74732012-01-01T00:00:00ZLAMARQUE, Claude-HenriTOUZÉ, CyrilTHOMAS, OlivierPerturbation methods are routinely used in all fields of applied mathematics where analytical solutions for nonlinear dynamical systems are searched. Among them, normal form theory provides a reliable method for systematically simplifying dynamical systems via nonlinear change of coordinates, and is also used in a mechanical context to define Nonlinear Normal Modes (NNMs). The main recognized drawback of perturbation methods is the absence of a criterion establishing their range of validity in terms of amplitude. In this paper, we propose a method to obtain upper bounds for amplitudes of changes of variables in normal form transformations. The criterion is tested on simple mechanical systems with one and two degrees-of-freedom, and for complex as well as real normal form. Its behavior with increasing order in the normal transform is established, and comparisons are drawn between exact solutions and normal form computations for increasing levels of amplitudes. The results clearly establish that the criterion gives an upper bound for validity limit of normal transforms.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.A new electrical circuit with negative capacitances to enhance resistive shunt damping
http://hdl.handle.net/10985/9985
A new electrical circuit with negative capacitances to enhance resistive shunt damping
BERARDENGO, Marta; MANZONI, Stefano; THOMAS, Olivier; GIRAUD-AUDINE, Christophe
This article proposes a new layout of electrical network based on two negative capacitance circuits, aimed at increasing the performances of a traditional resistive piezoelectric shunt for structural vibration reduction. It is equivalent to artificially increase the modal electromechanical coupling factor of the electromechanical structure by both decreasing the short-circuit natural frequencies and increasing the open-circuit ones. This leads to higher values of the modal electromechanical coupling factor with respect to simple negative capacitance configurations, when the same margin from stability is considered. This technique is shown to be powerful in enhancing the control performance when associated to a simple resistive shunt, usually avoided because of its poor performances.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/99852015-01-01T00:00:00ZBERARDENGO, MartaMANZONI, StefanoTHOMAS, OlivierGIRAUD-AUDINE, ChristopheThis article proposes a new layout of electrical network based on two negative capacitance circuits, aimed at increasing the performances of a traditional resistive piezoelectric shunt for structural vibration reduction. It is equivalent to artificially increase the modal electromechanical coupling factor of the electromechanical structure by both decreasing the short-circuit natural frequencies and increasing the open-circuit ones. This leads to higher values of the modal electromechanical coupling factor with respect to simple negative capacitance configurations, when the same margin from stability is considered. This technique is shown to be powerful in enhancing the control performance when associated to a simple resistive shunt, usually avoided because of its poor performances.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.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.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.PZT Nanofilm-Based Wafer Scale Nanoresonators
http://hdl.handle.net/10985/10206
PZT Nanofilm-Based Wafer Scale Nanoresonators
DEZEST, Denis; MATHIEU, Fabrice; MAZENQ, Laurent; SOYER, Caroline; COSTECALDE, Jean; THOMAS, Olivier; REMIENS, Denis
In this work, we present an unprecedented level of integration of piezoelectric actuation means on arrays of functional nanoresonators at the wafer scale. We use 150-nm thin lead titanate zirconate (PZT) as piezoelectric material mainly because of its excellent actuation properties even when geometrically constrained at extreme scale. This work paves promising ways for NEMS to be used in configurations where transduction capabilities are integrated at the nanodevice level providing effective fabrication process flow at the wafer-scale.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/102062015-01-01T00:00:00ZDEZEST, DenisMATHIEU, FabriceMAZENQ, LaurentSOYER, CarolineCOSTECALDE, JeanTHOMAS, OlivierREMIENS, DenisIn this work, we present an unprecedented level of integration of piezoelectric actuation means on arrays of functional nanoresonators at the wafer scale. We use 150-nm thin lead titanate zirconate (PZT) as piezoelectric material mainly because of its excellent actuation properties even when geometrically constrained at extreme scale. This work paves promising ways for NEMS to be used in configurations where transduction capabilities are integrated at the nanodevice level providing effective fabrication process flow at the wafer-scale.A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables
http://hdl.handle.net/10985/11412
A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables
COTTANCEAU, Emmanuel; THOMAS, Olivier; VERON, Philippe; ALOCHET, Marc; DELIGNY, Renaud
A flexible cable is modeled by a geometrically exact beam model with 3D rotations described using quaternion parameters. The boundary value problem is then discretized by the finite element method. The use of an asymptotic numerical method to solve the problem, quadratic equations, is well suited to the quaternion parametrization. This combination of methods leads to a fast, robust and accurate algorithm very well-adapted for the simulation of the assembly process of cables. This is proved by running many examples involving complicated solutions.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/114122016-01-01T00:00:00ZCOTTANCEAU, EmmanuelTHOMAS, OlivierVERON, PhilippeALOCHET, MarcDELIGNY, RenaudA flexible cable is modeled by a geometrically exact beam model with 3D rotations described using quaternion parameters. The boundary value problem is then discretized by the finite element method. The use of an asymptotic numerical method to solve the problem, quadratic equations, is well suited to the quaternion parametrization. This combination of methods leads to a fast, robust and accurate algorithm very well-adapted for the simulation of the assembly process of cables. This is proved by running many examples involving complicated solutions.Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams
http://hdl.handle.net/10985/11330
Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams
THOMAS, Olivier; SÉNÉCHAL, Aurélien; DEU, Jean-François
This work addresses the large amplitude nonlinear vibratory behavior of a rotating cantilever beam, with applications to turbomachinery and turbopropeller blades. The aim of this work is twofold. Firstly, we investigate the effect of rotation speed on the beam nonlinear vibrations and especially on the hardening/softening behavior of its resonances and the appearance of jump phenomena at large amplitude. Secondly, we compare three models to simulate the vibrations. The first two are based on analytical models of the beam, one of them being original. Those two models are discretized on appropriate mode basis and solve by a numerical following path method. The last one is based on a finite-element discretization and integrated in time. The accuracy and the validity range of each model are exhibited and analyzed.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/113302016-01-01T00:00:00ZTHOMAS, OlivierSÉNÉCHAL, AurélienDEU, Jean-FrançoisThis work addresses the large amplitude nonlinear vibratory behavior of a rotating cantilever beam, with applications to turbomachinery and turbopropeller blades. The aim of this work is twofold. Firstly, we investigate the effect of rotation speed on the beam nonlinear vibrations and especially on the hardening/softening behavior of its resonances and the appearance of jump phenomena at large amplitude. Secondly, we compare three models to simulate the vibrations. The first two are based on analytical models of the beam, one of them being original. Those two models are discretized on appropriate mode basis and solve by a numerical following path method. The last one is based on a finite-element discretization and integrated in time. The accuracy and the validity range of each model are exhibited and analyzed.