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3. Tuning and performance comparison of multiresonant piezoelectric shunts

Author

Ghislain Raze, Jennifer Dietrich, and Gaetan Kerschen

Subjects
Mechanical Engineering, General Materials Science
Abstract

This work presents tuning rules for piezoelectric shunts aiming to mitigate multiple structural resonances. Starting from a specification procedure of the shunt characteristics, the electrical parameters are derived for shunt topologies proposed in the literature, namely Hollkamp’s shunt, the current flowing shunt, the series parallel impedance structure and the current blocking shunt. Effective vibration mitigation of multiple structural modes is demonstrated numerically and experimentally on a piezoelectric beam. Performance in terms of vibration reduction obtained with the different shunts is shown to be comparable if similar shunt characteristics are considered.

Published
2022

4. Onset and stabilization of delay-induced instabilities in piezoelectric digital vibration absorbers

Author

Ghislain Raze, Jennifer Dietrich, and Gaetan Kerschen

Subjects
Mechanical Engineering, FOS: Mathematics, General Materials Science, Hardware_PERFORMANCEANDRELIABILITY, Dynamical Systems (math.DS), Mathematics - Dynamical Systems
Abstract

The stability of a piezoelectric structure controlled by a digital vibration absorber emulating a shunt circuit is investigated in this work. The formalism of feedback control theory is used to demonstrate that systems with a low electromechanical coupling are prone to delay-induced instabilities entailed by the sampling procedure of the digital unit. An explicit relation is derived between the effective electromechanical coupling factor and the maximum sampling period guaranteeing a stable controlled system. Since this sampling period may be impractically small, a simple modification procedure of the emulated admittance of the shunt circuit is proposed in order to counteract the effect of delays by anticipation. The theoretical developments are experimentally validated on a clamped-free piezoelectric beam.

Published
2022

6. Finite Element Model Upgrading of an Airplane Mockup with Nonlinear Attachments

Author

Giancarlo Kosova, Cristiano Dias Cunha, Emilio Di Lorenzo, Bart Peeters, Pedro Leal Ribeiro, Gaetan Kerschen, and Faculdade de Engenharia

Abstract

Nonlinear dynamic simulations of complex structures can have very high computational costs. In this work, a nonlinear modeling procedure is applied to an airplane mockup with two localized nonlinearities, connected to its wings. In order to reduce the simulation computational burden, the experimentally validated linear Finite Element Model (FEM) of the airplane is condensed into a Reduced Order Model (ROM). Only the modes with a relevant importance in the frequency range of interest are kept in the ROM. The linear ROM is then coupled with a local nonlinear data-driven model of the nonlinearities, obtaining a nonlinear ROM with relatively low computational weight. After using it for a nonlinear transient simulation, the physical answer in a desired node or point of interest can be obtained performing the inverse coordinate transformation. The local nonlinear data-driven model is based on the nonlinear attachments Restoring Force Surface (RFS), estimated through the Acceleration Surface Method (ASM). The nonlinear stiffness restoring force is modeled as a polynomial, estimated with a least square fitting of the experimental restoring force. The possibility to use this approach in case of multiple nonlinear modes is evaluated and the predictions of the model are compared with measured response.

Published
2022

9. Nonlinear Structures & Systems, Volume 1 : Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics 2020

Author

Gaetan Kerschen, Matthew R.W. Brake, Ludovic Renson, Gaetan Kerschen, Matthew R.W. Brake, and Ludovic Renson

Subjects
Statics, Nonlinear Optics, Civil engineering, Mechanics, Applied, Dynamics, Nonlinear theories
Abstract

Nonlinear Structures & Systems, Volume 1: Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020, the first volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on:Nonlinear Reduced-order ModelingJointed Structures: Identification, Mechanics, DynamicsExperimental Nonlinear DynamicsNonlinear Model & Modal InteractionsNonlinear DampingNonlinear Modeling & SimulationNonlinearity & System Identification

Published
2020

10. Nonlinear Structures and Systems, Volume 1 : Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics 2019

Author

Gaetan Kerschen, M. R. W. Brake, Ludovic Renson, Gaetan Kerschen, M. R. W. Brake, and Ludovic Renson

Subjects
Mechanics, Applied, Solids, Nonlinear Optics, Building materials
Abstract

Nonlinear Structures & Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics, 2019, the first volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Nonlinear Reduced-order Modeling Jointed Structures: Identification, Mechanics, Dynamics Experimental Nonlinear Dynamics Nonlinear Model & Modal Interactions Nonlinear Damping Nonlinear Modeling & Simulation Nonlinearity & System Identification

Published
2019

11. Nonlinear Dynamics, Volume 1 : Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018

Author

Gaetan Kerschen and Gaetan Kerschen

Subjects
Structural analysis (Engineering)--Congresses, Structural dynamics--Congresses, Nonlinear theories--Congresses
Abstract

Nonlinear Dynamics, Volume 1: Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018, the first volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Nonlinear System IdentificationNonlinear Modeling & SimulationNonlinear Reduced-order ModelingNonlinearity in PracticeNonlinearity in Aerospace SystemsNonlinearity in Multi-Physics SystemsNonlinear Modes and Modal InteractionsExperimental Nonlinear Dynamics

Published
2018

12. Nonlinear Dynamics, Volume 1 : Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics 2017

Author

Gaetan Kerschen and Gaetan Kerschen

Subjects
Engineering, Mechanics, Nonlinear mechanics--Congresses, Structural dynamics--Congresses, Vibration
Abstract

Nonlinear Dynamics, Volume 1: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics, 2017, the first volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Nonlinear System IdentificationNonlinear Modeling & SimulationNonlinear Reduced-order ModelingNonlinearity in PracticeNonlinearity in Aerospace SystemsNonlinearity in Multi-Physics SystemsNonlinear Modes and Modal InteractionsExperimental Nonlinear Dynamics

Published
2017

13. Nonlinear Dynamics, Volume 1 : Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015

Author

Gaëtan Kerschen and Gaëtan Kerschen

Subjects
Nonlinear mechanics--Congresses, Structural dynamics--Congresses
Abstract

Nonlinear Dynamics, Volume 1. Proceedings of the 33rd IMAC, A Conference and Exposition on Balancing Simulation and Testing, 2015, the first volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on:Nonlinear OscillationsNonlinear Simulation Using Harmonic BalanceNonlinear Modal AnalysisNonlinear System IdentificationNonlinear Modeling & SimulationNonlinearity in PracticeNonlinear SystemsRound Robin on Nonlinear System Identification.

Published
2016

14. Nonlinear Dynamics, Volume 2 : Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014

Author

Gaetan Kerschen and Gaetan Kerschen

Subjects
Structural dynamics--Congresses
Abstract

This second volume of eight from the IMAC - XXXII Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on:Linear SystemsSubstructure ModellingAdaptive StructuresExperimental TechniquesAnalytical MethodsDamage DetectionDamping of Materials & MembersModal Parameter IdentificationModal Testing MethodsSystem IdentificationActive ControlModal Parameter EstimationProcessing Modal Data

Published
2014

15. Modal Analysis of Nonlinear Mechanical Systems

Author

Gaetan Kerschen and Gaetan Kerschen

Subjects
Nonlinear mechanics
Abstract

The book first introduces the concept of nonlinear normal modes (NNMs) and their two main definitions. The fundamental differences between classical linear normal modes (LNMs) and NNMs are explained and illustrated using simple examples. Different methods for computing NNMs from a mathematical model are presented. Both advanced analytical and numerical methods are described. Particular attention is devoted to the invariant manifold and normal form theories. The book also discusses nonlinear system identification.

Published
2014

16. Topics in Nonlinear Dynamics, Volume 1 : Proceedings of the 31st IMAC, A Conference on Structural Dynamics, 2013

Author

Gaetan Kerschen, Douglas Adams, Alex Carrella, Gaetan Kerschen, Douglas Adams, and Alex Carrella

Subjects
Nonlinear mechanics--Congresses
Abstract

Topics in Nonlinear Dynamics, Volume 1: Proceedings of the 31st IMAC, A Conference and Exposition on Structural Dynamics, 2013, the first volume of seven from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Nonlinear OscillationsNonlinearities … In PracticeNonlinear System Identification: MethodsNonlinear System Identification: Friction & ContactNonlinear Modal AnalysisNonlinear Modeling & SimulationNonlinear Vibration AbsorbersConstructive Utilization of Nonlinearity

Published
2013

17. Detection, Modeling and Identification of Nonlinearities in Engineering Structures

Author

Gaetan Kerschen, Johan Schoukens, Bart Peeters, Alex Carrella, Jean-Philippe Noel, Wim Desmet, and Electricity

Subjects
Identification, detection, Modeling, nonlinearities
Abstract

Operational modal analysis from impulse response data can alternatively be viewed as an identification of a stable autonomous linear time-invariant system. For example, earthquake response data of civil engineering structures and impulsive excitation of bridges leads to this problem. Identification from a single experiment, however, does not yield a consistent estimator in the output error setting due to the exponential decay of the noise-free signal. Using data from multiple experiments, on the other hand, is not straightforward because of the need to match the initial conditions in the repeated experiments. Consequently, we consider the identification from arbitrary initial conditions and show that consistent estimation is possible in this case. The computational method proposed in the paper is based on analytic elimination of the initial conditions (nuisance parameter) and local optimization over the remaining (model) parameters. It is implemented in a ready to use software package, available from http://slra.github.io/software.html

Published
2014

19. Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems

Author

Alexander F. Vakakis, Oleg V. Gendelman, Lawrence A. Bergman, D. Michael McFarland, Gaëtan Kerschen, Young Sup Lee, Alexander F. Vakakis, Oleg V. Gendelman, Lawrence A. Bergman, D. Michael McFarland, Gaëtan Kerschen, and Young Sup Lee

Subjects
Energy transfer, Nonlinear systems
Abstract

This monograph evolved over a period of nine years from a series of papers and presentations addressing the subject of passive vibration control of mechanical s- tems subjected to broadband, transient inputs. The unifying theme is Targeted - ergy Transfer – TET, which represents a new and unique approach to the passive control problem, in which a strongly nonlinear, fully passive, local attachment, the Nonlinear Energy Sink – NES, is employed to drastically alter the dynamics of the primary system to which it is attached. The intrinsic capacity of the properly - signed NES to promote rapid localization of externally applied (narrowband) - bration or (broadband) shock energy to itself, where it can be captured and dis- pated, provides a powerful strategy for vibration control and the opens the pos- bility for a wide range of applications of TET, such as, vibration and shock i- lation, passive energy harvesting, aeroelastic instability (?utter) suppression, se- mic mitigation, vortex shedding control, enhanced reliability designs (for ex- ple in power grids) and others. The monograph is intended to provide a thorough explanation of the analytical, computational and experimental methods needed to formulate and study TET in mechanical and structural systems. Several prac- cal engineering applications are examined in detail, and experimental veri?cation and validation of the theoretical predictions are provided as well. The authors also suggest a number of possible future applications where application of TET seems promising. The authors are indebted to a number of sponsoring agencies.

Published
2008

20. Complex dynamics and targeted energy transfer in linear oscillators coupled to multi-degree-of-freedom essentially nonlinear attachments.

Author

Stylianos Tsakirtzis, Panagiotis Panagopoulos, Gaetan Kerschen, Oleg Gendelman, and Lawrence Bergman

Abstract

Abstract??We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment can passively absorb broadband energy from the linear system in a one-way, irreversible fashion, acting in essence as nonlinear energy sink (NES). Strong passive targeted energy transfer from the linear to the nonlinear subsystem is possible over wide frequency and energy ranges. In an effort to study the dynamics of the coupled system of oscillators, we study numerically and analytically the periodic orbits of the corresponding undamped and unforced hamiltonian system with asymptotics and reduction. We prove the existence of a family of countable infinity of periodic orbits that result from combined parametric and external resonance interactions of the masses of the NES. We numerically demonstrate that the topological structure of the periodic orbits in the frequency?energy plane of the hamiltonian system greatly influences the strength of targeted energy transfer in the damped system and, to a great extent, governs the overall transient damped dynamics. This work may be regarded as a contribution towards proving the efficacy the utilizing essentially nonlinear attachments as passive broadband boundary controllers. [ABSTRACT FROM AUTHOR]

Published
2007
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21. Energy Transfers in a System of Two Coupled Oscillators with Essential Nonlinearity: 1:1 Resonance Manifold and Transient Bridging Orbits.

Author

Gaetan Kerschen, Alexander Vakakis, Young Lee, D. Mcfarland, Jeffrey Kowtko, and Lawrence Bergman

Abstract

The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator weakly coupled to an essentially nonlinear attachment, termed a nonlinear energy sink. Although these energy exchanges are encountered during the transient dynamics of the damped system, it is shown that the dynamics can be interpreted mainly in terms of the periodic orbits of the underlying Hamiltonian system. To this end, a frequency-energy plot gathering the periodic orbits of the system is constructed which demonstrates that, thanks to a 1:1 resonance capture, energy can be irreversibly and almost completely transferred from the linear oscillator to the nonlinear attachment. Furthermore, it is observed that this nonlinear energy pumping is triggered by the excitation of transient bridging orbits compatible with the nonlinear attachment being initially at rest, a common feature in most practical applications. A parametric study of the energy exchanges is also performed to understand the influence of the parameters of the nonlinear energy sink. Finally, the results of experimental measurements supporting the theoretical developments are discussed. [ABSTRACT FROM AUTHOR]

Published
2005
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22. The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview.

Author

Gaetan Kerschen, Jean-claude Golinval, ALEXANDER F. VAKAKIS, and LAWRENCE A. BERGMAN

Abstract

Abstract Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theory based on nonlinear normal modes is indubitably the most appealing. In this paper, a different approach is adopted, and proper orthogonal decomposition is considered. The modes extracted from the decomposition may serve two purposes, namely order reduction by projecting high-dimensional data into a lower-dimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data. The utility of the method for dynamic characterization and order reduction of linear and nonlinear mechanical systems is demonstrated in this study. [ABSTRACT FROM AUTHOR]

Published
2005
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23. Generation of Accurate Finite Element Models of Nonlinear Systems – Application to an Aeroplane-Like Structure.

Author

Gaetan Kerschen and Jean-Claude Golinval

Abstract

Abstract Model updating and validation is currently a central issue in the fields of computational structural mechanics and dynamics. The vast majority of applications however concerns linear structures. On the other hand, updating nonlinear models is something the structural dynamicist prefers to avoid mainly because tools such as modal analysis are no longer available. The objective of the present study is to propose a two-step methodology for dealing with nonlinear systems. Its most appealing feature is that it decouples the estimation of the linear and nonlinear parameters. A numerical application consisting of an aeroplane-like structure is used to assess the efficiency of the procedure. [ABSTRACT FROM AUTHOR]

Published
2005
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24. Enforcing a Force–Displacement Curve of a Nonlinear Structure Using Topology Optimization with Slope Constraints

Author

Jongsuh Lee, Thibaut Detroux, and Gaëtan Kerschen

Subjects
force–displacement curve, topology optimization, hardening and softening nonlinearities, slope constraint, Technology, Engineering (General). Civil engineering (General), TA1-2040, Biology (General), QH301-705.5, Physics, QC1-999, Chemistry, QD1-999
Abstract

The objective of this study is to develop an optimization methodology to find a layout that traces a prescribed force–displacement curve through a topology optimization approach. To this end, we propose an objective function to minimize the difference between a prescribed force–displacement curve and the curve calculated at each iteration of the optimization process. Slope constraints are introduced to solve issues encountered when using a small number of target points. In addition, a projection filter is employed to suppress the gray region observed between the solid and void regions, which generally occurs when using a density-based filter. A recently proposed energy interpolation scheme is implemented to stabilize the instability in the nonlinear analysis, which generally results from excessive distortion in the void region when the structure is modeled on a fixed mesh in the topology optimization process. To validate the outlined methodology, several case studies with different types of nonlinearity and structural features of the obtained layouts are investigated.

Published
2020
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25. Experimental study of isolas in nonlinear systems featuring modal interactions.

Author

Thibaut Detroux, Jean-Philippe Noël, Lawrence N Virgin, and Gaëtan Kerschen

Subjects
Medicine, Science
Abstract

The objective of the present paper is to provide experimental evidence of isolated resonances in the frequency response of nonlinear mechanical systems. More specifically, this work explores the presence of isolas, which are periodic solutions detached from the main frequency response, in the case of a nonlinear set-up consisting of two masses sliding on a horizontal guide. A careful experimental investigation of isolas is carried out using responses to swept-sine and stepped-sine excitations. The experimental findings are validated with advanced numerical simulations combining nonlinear modal analysis and bifurcation monitoring. In particular, the interactions between two nonlinear normal modes are shown to be responsible for the creation of the isolas.

Published
2018
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26. A nonlinear state-space solution to a hysteretic benchmark in system identification

Author

Jean-Philippe Noel, Gaetan Kerschen, Alireza Fakhrizadeh Esfahani, Johan Schoukens, Electricity, Faculty of Engineering, and Thermodynamics and Fluid Mechanics Group

Subjects
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, MathematicsofComputing_NUMERICALANALYSIS
Abstract

The present contribution addresses the identification of the hysteretic benchmark introduced in Ref. [1]. To this end, a discrete-time nonlinear state-space model is built considering multivariate polynomial terms in the state equation.

27. Acoustic mitigation

Author

Bruno Cochelin, Matériaux et Structures (M&S), Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM), Gaetan Kerschen, and Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SPI]Engineering Sciences [physics], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2014

28. Numerical computation of nonlinear normal modes using HBM and ANM

Author

Bruno Cochelin, Matériaux et Structures (M&S), Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM), Gaetan Kerschen, and Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Computer science, Numerical analysis, Computation, Modal analysis, 02 engineering and technology, Bifurcation diagram, 01 natural sciences, Nonlinear system, Harmonic balance, Continuation, [SPI]Engineering Sciences [physics], 020303 mechanical engineering & transports, 0203 mechanical engineering, Normal mode, 0103 physical sciences, Applied mathematics, 010301 acoustics, ComputingMilieux_MISCELLANEOUS
Abstract

These notes correspond to the four lectures given by Bruno Cochelin at the CISM course on “Modal Analysis of Nonlinear Mechanical Systems” held at Udine, from 25 to 29 june 2012. The goal is to describe numerical methods which are complementary to those presented in the previous chapter by Gaetan Kerschen. Once again a conservative nonlinear normal mode will be seen as a one-parameter familly of periodic orbits. The Harmonic Balance Method (HBM) will be used for computing periodic solutions and the Asymptotic Numerical Method (ANM) will be used for the continuation of these periodic solutions. The methods and the results presented above have been obtained with the collaboration of S. Bellizzi, S. Karkar, E.H. Moussi and C. Vergez.

Published
2014

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