Experimental study of isolas in nonlinear systems featuring modal interactions

[en] 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.

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

Detroux, Thibaut ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Noël, Jean-Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Virgin, Lawrence; Duke University > Pratt School of Engineering

Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Language :

English

Title :

Experimental study of isolas in nonlinear systems featuring modal interactions

Publication date :

27 March 2018

Journal title :

PLoS ONE

eISSN :

1932-6203

Publisher :

Public Library of Science, United States - California

Volume :

Issue :

Pages :

e0194452

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
UE - Union Européenne [BE]

Available on ORBi :

since 23 January 2018

Statistics

Number of views

100 (18 by ULiège)

Number of downloads

97 (11 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

Bibliography

Mehrabi M.H., Suhatril M., Ibrahim Z., Ghodsi S.S., Khatibi H. Modeling of a viscoelastic damper and its application in structural control. PloS one, 12(6):e0176480, 2017. https://doi.org/10.1371/journal.pone. 0176480 PMID: 28570657
Lossouarn B., DeüJ.F., Aucejo M. Multimodal vibration damping of a beam with a periodic array of piezoelectric patches connected to a passive electrical network. Smart Materials and Structures, 24 (11):115037, 2015. https://doi.org/10.1088/0964-1726/24/11/115037
Nayfeh A.H., Mook D.T. Nonlinear Oscillations. John Wiley & Sons, New-York, NY, 2008.
Seydel R. Practical bifurcation and stability analysis. Springer-Verlag, New-York, NY, 2010.
Gatti G., Brennan M.J., Kovacic I. On the interaction of the responses at the resonance frequencies of a nonlinear two degrees-of-freedom system. Physica D: Nonlinear Phenomena, 239(10):591-599, 2010.https://doi.org/10.1016/j.physd.2010.01.006
Alexander N.A., Schilder F. Exploring the performance of a nonlinear tuned mass damper. Journal of Sound and Vibration, 319(1):445-462, 2009. https://doi.org/10.1016/j.jsv.2008.05.018
Duan C., Singh R. Isolated sub-harmonic resonance branch in the frequency response of an oscillator with slight asymmetry in the clearance. Journal of Sound and Vibration, 314(1):12-18, 2008. https://doi.org/10.1016/j.jsv.2007.12.040
Koenigsberg W., Dunn J. Jump resonant frequency islands in nonlinear feedback control systems. IEEE Transactions on Automatic Control, 20(2):208-217, 1975. https://doi.org/10.1109/TAC.1975. 1100914
Detroux T., Renson L., Masset L., Kerschen G. The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems. Computer Methods in Applied Mechanics and Engineering, 296:18-38, 2015. https://doi.org/10.1016/j.cma.2015.07.017
Gourc E., Michon G., Seguy S., Berlioz A. Experimental investigation and design optimization of targeted energy transfer under periodic forcing. Journal of Vibration and Acoustics, 136(2):021021, 2014. https://doi.org/10.1115/1.4026432
Starosvetsky Y., Gendelman O.V. Vibration absorption in systems with a nonlinear energy sink: Nonlinear damping. Journal of Sound and Vibration, 324(3):916-939, 2009. https://doi.org/10.1016/j.jsv. 2009.02.052
Takács D. and Stépán G., Hogan S.J. Isolated large amplitude periodic motions of towed rigid wheels. Nonlinear Dynamics, 52(1-2):27-34, 2008. https://doi.org/10.1007/s11071-007-9253-y
Sarrouy E., Grolet A., Thouverez F. Global and bifurcation analysis of a structure with cyclic symmetry. International Journal of Non-Linear Mechanics, 46(5):727-737, 2011. https://doi.org/10.1016/j.ijnonlinmec.2011.02.005
Géradin M., Rixen D.J. Mechanical Vibrations: Theory and Application to Structural Dynamics. John Wiley & Sons, New-York, NY, 2014.
Rosenberg R.M. On nonlinear vibrations of systems with many degrees of freedom. Advances in Applied Mechanics, 9(155-242):6-1, 1966.
Kerschen G., Peeters M., Golinval J.C., Vakakis A.F. Nonlinear normal modes, Part I: A useful framework for the structural dynamicist. Mechanical Systems and Signal Processing, 23(1):170-194, 2009. https://doi.org/10.1016/j.ymssp.2008.04.002
Avramov K.V., Mikhlin Y.V. Review of applications of nonlinear normal modes for vibrating mechanical systems. Applied Mechanics Reviews, 65(2):020801, 2013. https://doi.org/10.1115/1.4023533
Shaw A.D., Hill T.L., Neild S.A., Friswell M.I. Periodic responses of a structure with 3:1 internal resonance. Mechanical Systems and Signal Processing, 81:19-34, 2016. https://doi.org/10.1016/j.ymssp. 2016.03.008
Mangussi F., Zanette D.H. Internal resonance in a vibrating beam: a zoo of nonlinear resonance peaks. PloS ONE, 11(9):e0162365, 2016. https://doi.org/10.1371/journal.pone.0162365 PMID: 27648829
Kuether R.J., Renson L., Detroux T., Grappasonni C., Kerschen G., Allen M.S. Nonlinear normal modes, modal interactions and isolated resonance curves. Journal of Sound and Vibration, 351:299- 310, 2015. https://doi.org/10.1016/j.jsv.2015.04.035
George C., Virgin L.N., Witelski T. Experimental study of regular and chaotic transients in a non-smooth system. International Journal of Non-Linear Mechanics, 81:55-64, 2016. https://doi.org/10.1016/j.ijnonlinmec.2015.12.006
Gatti G., Brennan M.J. Inner detached frequency response curves: an experimental study. Journal of Sound and Vibration, 396:246-254, 2017. https://doi.org/10.1016/j.jsv.2017.02.008
Virgin L.N. Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration. Cambridge University Press, Cambridge, United Kingdom, 2000.
Vakakis A.F., Manevitch L.I., Mikhlin Y.V., Pilipchuk V.N., Zevin A.A. Normal Modes and Localization in Nonlinear Systems. John Wiley & Sons, New-York, NY, 2008.
Hill T.L., Cammarano A., Neild S.A., Wagg D.J. Interpreting the forced responses of a two-degree-offreedom nonlinear oscillator using backbone curves. Journal of Sound and Vibration, 349:276-288, 2015. https://doi.org/10.1016/j.jsv.2015.03.030
Hill T.L., Neild S.A., Cammarano A. An analytical approach for detecting isolated periodic solution branches in weakly nonlinear structures. Journal of Sound and Vibration, 379:150-165, 2016. https://doi.org/10.1016/j.jsv.2016.05.030
Antonio D., Zanette D.H., López D. Frequency stabilization in nonlinear micromechanical oscillators. Nature Communications, 3:806, 2012. https://doi.org/10.1038/ncomms1813 PMID: 22549835
Barton D.A.W., Mann B.P., Burrow S.G. Control-based continuation for investigating nonlinear experiments. Journal of Vibration and Control, 18(4):509-520, 2012. https://doi.org/10.1177/1077546310384004
Sieber J., Krauskopf B. Control based bifurcation analysis for experiments. Nonlinear Dynamics, 51(3):365-377, 2008. https://doi.org/10.1007/s11071-007-9217-2