Nonlinear normal modes modal interactions and isolated resonance curves

Kuether, Robert J.; Renson, L.; Detroux, T.; Grappasonni, C.; Kerschen, G.; Allen, M. S.

doi:10.1016/j.jsv.2015.04.035

Title: Nonlinear normal modes modal interactions and isolated resonance curves

Journal Article · Thu May 21 00:00:00 EDT 2015 · Journal of Sound and Vibration

DOI:https://doi.org/10.1016/j.jsv.2015.04.035· OSTI ID:1237470

Kuether, Robert J. ^[1]; Renson, L. ^[2]; Detroux, T. ^[2]; Grappasonni, C. ^[2]; Kerschen, G. ^[2]; Allen, M. S. ^[1]

Univ. of Wisconsin, Madison, WI (United States)
Univ. of Liege, Liege (Belgium)

The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system. To this end, an energy balance technique is used to predict the amplitude of the harmonic forcing that is necessary to excite a specific nonlinear normal mode. A cantilever beam with a nonlinear spring at its tip serves to illustrate the developments. Furthermore, the practical implications of isolated resonance curves are also discussed by computing the beam response to sine sweep excitations of increasing amplitudes.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1237470

Report Number(s):: SAND-2015-2504J; 579836

Journal Information:: Journal of Sound and Vibration, Vol. 351, Issue C; ISSN 0022-460X

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 74 works

Citation information provided by
Web of Science

References (38)

A Soft-Landing Waveform for Actuation of a Single-Pole Single-Throw Ohmic RF MEMS Switch Czaplewski, David A.; Dyck, Christopher W.; Sumali, Hartono Journal of Microelectromechanical Systems, Vol. 15, Issue 6 https://doi.org/10.1109/JMEMS.2006.883576	journal	January 2006
The Simplest Walking Model: Stability, Complexity, and Scaling Garcia, Mariano; Chatterjee, Anindya; Ruina, Andy Journal of Biomechanical Engineering, Vol. 120, Issue 2 https://doi.org/10.1115/1.2798313	journal	April 1998
Bifurcations of Nonlinear Normal Modes of Linear Oscillator with Strongly Nonlinear Damped Attachment Gendelman, Oleg V. Nonlinear Dynamics, Vol. 37, Issue 2 https://doi.org/10.1023/B:NODY.0000042911.49430.25	journal	July 2004
Isolated Resonance Captures and Resonance Capture Cascades Leading to Single- or Multi-Mode Passive Energy Pumping in Damped Coupled Oscillators Vakakis, Alexander F.; McFarland, D. Michael; Bergman, Lawrence Journal of Vibration and Acoustics, Vol. 126, Issue 2 https://doi.org/10.1115/1.1687397	journal	April 2004
Epistemic and Aleatoric Uncertainty in Modeling Segalman, Daniel J.; Brake, Matthew R.; Bergman, Lawrence A. ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Volume 8: 22nd Reliability, Stress Analysis, and Failure Prevention Conference; 25th Conference on Mechanical Vibration and Noise https://doi.org/10.1115/DETC2013-13234	conference	February 2014
Normal Modes of Nonlinear Dual-Mode Systems Rosenberg, R. M. Journal of Applied Mechanics, Vol. 27, Issue 2 https://doi.org/10.1115/1.3643948	journal	June 1960
Normal Modes for Non-Linear Vibratory Systems Shaw, S. W.; Pierre, C. Journal of Sound and Vibration, Vol. 164, Issue 1 https://doi.org/10.1006/jsvi.1993.1198	journal	June 1993
NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW Vakakis, A. F. Mechanical Systems and Signal Processing, Vol. 11, Issue 1 https://doi.org/10.1006/mssp.1996.9999	journal	January 1997
Nonlinear normal modes, Part I: A useful framework for the structural dynamicist Kerschen, G.; Peeters, M.; Golinval, J. C. Mechanical Systems and Signal Processing, Vol. 23, Issue 1 https://doi.org/10.1016/j.ymssp.2008.04.002	journal	January 2009
Nonlinear normal modes of structural systems via asymptotic approach Lacarbonara, Walter; Camillacci, Rodolfo International Journal of Solids and Structures, Vol. 41, Issue 20 https://doi.org/10.1016/j.ijsolstr.2004.04.029	journal	October 2004
Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures Touzé, C.; Amabili, M. Journal of Sound and Vibration, Vol. 298, Issue 4-5 https://doi.org/10.1016/j.jsv.2006.06.032	journal	December 2006
Two methods for the computation of nonlinear modes of vibrating systems at large amplitudes Arquier, Rémi; Bellizzi, Sergio; Bouc, Robert Computers & Structures, Vol. 84, Issue 24-25 https://doi.org/10.1016/j.compstruc.2006.01.011	journal	September 2006
A numerical approach to directly compute nonlinear normal modes of geometrically nonlinear finite element models Kuether, Robert J.; Allen, Matthew S. Mechanical Systems and Signal Processing, Vol. 46, Issue 1 https://doi.org/10.1016/j.ymssp.2013.12.010	journal	May 2014
Complex non-linear modal analysis for mechanical systems: Application to turbomachinery bladings with friction interfaces Laxalde, Denis; Thouverez, Fabrice Journal of Sound and Vibration, Vol. 322, Issue 4-5 https://doi.org/10.1016/j.jsv.2008.11.044	journal	May 2009
Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques Peeters, M.; Viguié, R.; Sérandour, G. Mechanical Systems and Signal Processing, Vol. 23, Issue 1 https://doi.org/10.1016/j.ymssp.2008.04.003	journal	January 2009
A new Galerkin-Based Approach for Accurate Non-Linear Normal Modes Through Invariant Manifolds Pesheck, E.; Pierre, C.; Shaw, S. W. Journal of Sound and Vibration, Vol. 249, Issue 5 https://doi.org/10.1006/jsvi.2001.3914	journal	January 2002
An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems Renson, L.; Deliége, G.; Kerschen, G. Meccanica, Vol. 49, Issue 8 https://doi.org/10.1007/s11012-014-9875-3	journal	January 2014
Nonlinear Modal Analysis of a Full-Scale Aircraft Kerschen, G.; Peeters, M.; Golinval, J. C. Journal of Aircraft, Vol. 50, Issue 5 https://doi.org/10.2514/1.C031918	journal	September 2013
A method for nonlinear modal analysis and synthesis: Application to harmonically forced and self-excited mechanical systems Krack, Malte; Panning-von Scheidt, Lars; Wallaschek, Jörg Journal of Sound and Vibration, Vol. 332, Issue 25 https://doi.org/10.1016/j.jsv.2013.08.009	journal	December 2013
Complex dynamics of a nonlinear aerospace structure: numerical continuation and normal modes Renson, L.; Noël, J. P.; Kerschen, G. Nonlinear Dynamics, Vol. 79, Issue 2 https://doi.org/10.1007/s11071-014-1743-0	journal	October 2014
Dynamic testing of nonlinear vibrating structures using nonlinear normal modes Peeters, M.; Kerschen, G.; Golinval, J. C. Journal of Sound and Vibration, Vol. 330, Issue 3 https://doi.org/10.1016/j.jsv.2010.08.028	journal	January 2011
Modal testing of nonlinear vibrating structures based on nonlinear normal modes: Experimental demonstration Peeters, M.; Kerschen, G.; Golinval, J. C. Mechanical Systems and Signal Processing, Vol. 25, Issue 4 https://doi.org/10.1016/j.ymssp.2010.11.006	journal	May 2011
Nonlinear modal identification of a steel frame Zapico-Valle, J. L.; García-Diéguez, M.; Alonso-Camblor, R. Engineering Structures, Vol. 56 https://doi.org/10.1016/j.engstruct.2013.04.026	journal	November 2013
Bifurcations of backbone curves for systems of coupled nonlinear two mass oscillator Cammarano, A.; Hill, T. L.; Neild, S. A. Nonlinear Dynamics, Vol. 77, Issue 1-2 https://doi.org/10.1007/s11071-014-1295-3	journal	February 2014
Bifurcation analysis of a parametrically excited inclined cable close to two-to-one internal resonance Marsico, M. R.; Tzanov, V.; Wagg, D. J. Journal of Sound and Vibration, Vol. 330, Issue 24 https://doi.org/10.1016/j.jsv.2011.07.027	journal	November 2011
On the interaction of the responses at the resonance frequencies of a nonlinear two degrees-of-freedom system Gatti, Gianluca; Brennan, Michael J.; Kovacic, Ivana Physica D: Nonlinear Phenomena, Vol. 239, Issue 10 https://doi.org/10.1016/j.physd.2010.01.006	journal	May 2010
On the effects of system parameters on the response of a harmonically excited system consisting of weakly coupled nonlinear and linear oscillators Gatti, Gianluca; Brennan, Michael J. Journal of Sound and Vibration, Vol. 330, Issue 18-19 https://doi.org/10.1016/j.jsv.2011.04.006	journal	August 2011
Exploring the performance of a nonlinear tuned mass damper Alexander, Nicholas A.; Schilder, Frank Journal of Sound and Vibration, Vol. 319, Issue 1-2 https://doi.org/10.1016/j.jsv.2008.05.018	journal	January 2009
Isolated sub-harmonic resonance branch in the frequency response of an oscillator with slight asymmetry in the clearance Duan, Chengwu; Singh, Rajendra Journal of Sound and Vibration, Vol. 314, Issue 1-2 https://doi.org/10.1016/j.jsv.2007.12.040	journal	July 2008
Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves Hill, T. L.; Cammarano, A.; Neild, S. A. Journal of Sound and Vibration, Vol. 349 https://doi.org/10.1016/j.jsv.2015.03.030	journal	August 2015
Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment Lee, Young Sup; Kerschen, Gaetan; Vakakis, Alexander F. Physica D: Nonlinear Phenomena, Vol. 204, Issue 1-2 https://doi.org/10.1016/j.physd.2005.03.014	journal	May 2005
A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions Cochelin, Bruno; Vergez, Christophe Journal of Sound and Vibration, Vol. 324, Issue 1-2 https://doi.org/10.1016/j.jsv.2009.01.054	journal	July 2009
Numerical Continuation of Periodic Orbits for Harmonically Forced Nonlinear Systems Sracic, Michael W.; Allen, Matthew S. Civil Engineering Topics, Volume 4 https://doi.org/10.1007/978-1-4419-9316-8_5	book	January 2011
Computing Nonlinear Normal Modes Using Numerical Continuation and Force Appropriation Kuether, Robert J.; Allen, Matthew S. ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Volume 1: 24th Conference on Mechanical Vibration and Noise, Parts A and B https://doi.org/10.1115/DETC2012-71257	conference	September 2013
The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems Detroux, T.; Renson, L.; Masset, L. Computer Methods in Applied Mechanics and Engineering, Vol. 296 https://doi.org/10.1016/j.cma.2015.07.017	journal	November 2015
Electron Reconstruction and Identification with the ATLAS Detector Kerschen, Nicolas Proceedings of European Physical Society Europhysics Conference on High Energy Physics — PoS(EPS-HEP 2009) https://doi.org/10.22323/1.084.0429	conference	June 2010
A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions Cochelin, Bruno; Vergez, Christophe arXiv https://doi.org/10.48550/arxiv.0808.3839	text	January 2008
A method for nonlinear modal analysis and synthesis: Application to harmonically forced and self-excited mechanical systems Krack, Malte; Scheidt, Lars Panning-von; Wallaschek, Jörg arXiv https://doi.org/10.48550/arxiv.2101.01804	text	January 2021

Cited By (17)

Detection and Quantification of Non-Linear Structural Behavior Using Frequency Domain Methods Prawin, J.; Rao, A. Rama Mohan Research in Nondestructive Evaluation, Vol. 31, Issue 2 https://doi.org/10.1080/09349847.2019.1623958	journal	June 2019
Experimental Tracking of Limit-Point Bifurcations and Backbone Curves Using Control-Based Continuation Renson, Ludovic; Barton, David A. W.; Neild, Simon A. International Journal of Bifurcation and Chaos, Vol. 27, Issue 01 https://doi.org/10.1142/s0218127417300026	journal	January 2017
Vibration Prediction of Bladed Disks Coupled by Friction Joints Krack, Malte; Salles, Loic; Thouverez, Fabrice Archives of Computational Methods in Engineering, Vol. 24, Issue 3 https://doi.org/10.1007/s11831-016-9183-2	journal	July 2016
Bayesian model updating of nonlinear systems using nonlinear normal modes Song, Mingming; Renson, Ludovic; Noël, Jean-Philippe Structural Control and Health Monitoring, Vol. 25, Issue 12 https://doi.org/10.1002/stc.2258	journal	September 2018
Period doubling bifurcation analysis and isolated sub-harmonic resonances in an oscillator with asymmetric clearances Alcorta, Roberto; Baguet, Sebastien; Prabel, Benoit Nonlinear Dynamics, Vol. 98, Issue 4 https://doi.org/10.1007/s11071-019-05245-6	journal	September 2019
Identifying the significance of nonlinear normal modes Hill, T. L.; Cammarano, A.; Neild, S. A. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, Issue 2199 https://doi.org/10.1098/rspa.2016.0789	journal	March 2017
Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction Haller, George; Ponsioen, Sten Nonlinear Dynamics, Vol. 86, Issue 3 https://doi.org/10.1007/s11071-016-2974-z	journal	August 2016
Nonlinear polarization coupling in freestanding nanowire/nanotube resonators Vincent, P.; Descombin, A.; Dagher, S. Journal of Applied Physics, Vol. 125, Issue 4 https://doi.org/10.1063/1.5053955	journal	January 2019
Experimental study of isolas in nonlinear systems featuring modal interactions Detroux, Thibaut; Noël, Jean-Philippe; Virgin, Lawrence N. PLOS ONE, Vol. 13, Issue 3 https://doi.org/10.1371/journal.pone.0194452	journal	March 2018
Isolated resonances and nonlinear damping Habib, Giuseppe; Cirillo, Giuseppe I.; Kerschen, Gaetan Nonlinear Dynamics, Vol. 93, Issue 3 https://doi.org/10.1007/s11071-018-4240-z	journal	April 2018
Conditions for the existence of isolated backbone curves Hong, Dongxiao; Hill, Thomas L.; Neild, Simon A. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 475, Issue 2232 https://doi.org/10.1098/rspa.2019.0374	journal	December 2019
Global detection of detached periodic solution branches of friction-damped mechanical systems Heinze, Torsten; Panning-von Scheidt, Lars; Wallaschek, Jörg Nonlinear Dynamics, Vol. 99, Issue 3 https://doi.org/10.1007/s11071-019-05425-4	journal	December 2019
On Nonlinear Motions of Two-Degree-of-Freedom Nonlinear Systems with Repeated Linearized Natural Frequencies An, Hua-Zhen; Yang, Xiao-Dong; Liang, Feng International Journal of Bifurcation and Chaos, Vol. 29, Issue 10 https://doi.org/10.1142/s0218127419501323	journal	September 2019
Isolated resonances and nonlinear damping Habib, Giuseppe; Cirillo, Giuseppe Ilario; Kerschen, Gaetan arXiv https://doi.org/10.48550/arxiv.1707.03561	preprint	January 2017
Force appropriation of nonlinear structures Renson, L.; Hill, T. L.; Ehrhardt, D. A. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 474, Issue 2214 https://doi.org/10.1098/rspa.2017.0880	journal	June 2018
Application of control-based continuation to a nonlinear structure with harmonically coupled modes Renson, L.; Shaw, A. D.; Barton, D. A. W. arXiv https://doi.org/10.48550/arxiv.1808.01865	text	January 2018
Stability of Forced-Damped Response in Mechanical Systems from a Melnikov Analysis Cenedese, Mattia; Haller, George arXiv https://doi.org/10.48550/arxiv.2005.00444	text	January 2020

Similar Records

Relationships between nonlinear normal modes and response to random inputs

Journal Article · Mon Jul 25 00:00:00 EDT 2016 · Mechanical Systems and Signal Processing · OSTI ID:1237470

Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

Multi-mode quasi-static excitation for systems with nonlinear joints

Journal Article · Wed Feb 15 00:00:00 EST 2023 · Mechanical Systems and Signal Processing · OSTI ID:1237470

Singh, Aabhas; Allen, Matthew S.; Kuether, Robert J.

Physical mechanisms of megahertz vibrations and nonlinear detection in ultrasonic force and related microscopies

Journal Article · Mon Apr 14 00:00:00 EDT 2014 · Journal of Applied Physics · OSTI ID:1237470

Bosse, J. L.; Huey, B. D.; Tovee, P. D.

Related Subjects

42 ENGINEERING
nonlinear normal modes
modal interaction
nonlinear forced response
isolated resonance curves
fold bifurcations

Title: Nonlinear normal modes modal interactions and isolated resonance curves

Citation Formats

References (38)

Cited By (17)

Similar Records

Related Subjects