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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 16 Nov 2019 00:59:40 GMT2019-11-16T00:59:40ZIdentification of mode couplings in nonlinear vibrations of the steelpan
http://hdl.handle.net/10985/8943
Identification of mode couplings in nonlinear vibrations of the steelpan
MONTEIL, Mélodie; THOMAS, Olivier; TOUZÉ, Cyril
The vibrations and sounds produced by two notes of a double second steelpan are investigated, the main objective being to quantify the nonlinear energy exchanges occurring between vibration modes that are responsible of the peculiar sound of the instrument. A modal analysis first reveals the particular tuning of the modes and the systematic occurence of degenerate modes, from the second one, this feature being a consequence of the tuning and the mode localization. Forced vibrations experiments are then performed to follow precisely the energy exchange between harmonics of the vibration and thus quantify properly the mode couplings. In particular, it is found that energy exchanges are numerous, resulting in complicated frequency response curves even for very small levels of vibration amplitude. Simple models displaying 1:2:2 and 1:2:4 internal resonance are then fitted to the measurements, allowing to identify the values of the nonlinear quadratic coupling coefficients resulting from the geometric nonlinearity. The identified 1:2:4 model is finally used to recover the time domain variations of an impacted note in normal playing condition, resulting in an excellent agreement for the temporal behaviour of the first four harmonics.
The authors are grateful to Bertrand David (Telecom-ParisTech) for computing the code allowing the STFT filtering procedure used in Section 5.1. The filter has been designed in the framework of the PAFI project (Plateforme d’Aide la facture Instrumentale, www.pafi.fr) which is also thanked.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/89432015-01-01T00:00:00ZMONTEIL, MélodieTHOMAS, OlivierTOUZÉ, CyrilThe vibrations and sounds produced by two notes of a double second steelpan are investigated, the main objective being to quantify the nonlinear energy exchanges occurring between vibration modes that are responsible of the peculiar sound of the instrument. A modal analysis first reveals the particular tuning of the modes and the systematic occurence of degenerate modes, from the second one, this feature being a consequence of the tuning and the mode localization. Forced vibrations experiments are then performed to follow precisely the energy exchange between harmonics of the vibration and thus quantify properly the mode couplings. In particular, it is found that energy exchanges are numerous, resulting in complicated frequency response curves even for very small levels of vibration amplitude. Simple models displaying 1:2:2 and 1:2:4 internal resonance are then fitted to the measurements, allowing to identify the values of the nonlinear quadratic coupling coefficients resulting from the geometric nonlinearity. The identified 1:2:4 model is finally used to recover the time domain variations of an impacted note in normal playing condition, resulting in an excellent agreement for the temporal behaviour of the first four harmonics.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.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.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.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.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.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.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.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.