Phase resonance nonlinear modes of mechanical systems

Volvert, Martin; Kerschen, Gaëtan

doi:10.1016/j.jsv.2021.116355

Request a copy

Article (Scientific journals)

Phase resonance nonlinear modes of mechanical systems

Volvert, Martin; Kerschen, Gaëtan

2021 • In Journal of Sound and Vibration, 511, p. 116355

Peer Reviewed verified by ORBi

Permalink
https://hdl.handle.net/2268/262452

DOI
10.1016/j.jsv.2021.116355

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

1-s2.0-S0022460X21004119-main.pdf

Publisher postprint (2.34 MB)

Request a copy

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Nonlinear Dynamics; Phase resonance; Modal analysis

Abstract :

[en] The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase resonance of nonlinear mechanical systems subjected to single-point, single-harmonic excitation. In this context, the main contribution of this paper is to develop a computational framework which can predict the mode shapes and oscillation frequencies at phase resonance. The resulting nonlinear modes are termed phase resonance nonlinear modes (PRNMs). A key property of PRNMs is that, besides primary resonances, they can accurately characterize superharmonic, subharmonic and ultra-subharmonic resonances for which, as shall be shown in this paper, phase lags at resonance may be different from 𝜋∕2. The proposed developments are demonstrated using one- and two-degree-of-freedom systems featuring a cubic nonlinearity.

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

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

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

Language :

English

Title :

Phase resonance nonlinear modes of mechanical systems

Publication date :

27 October 2021

Journal title :

Journal of Sound and Vibration

ISSN :

0022-460X

eISSN :

1095-8568

Publisher :

Elsevier, United States

Volume :

511

Pages :

116355

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 09 August 2021

Statistics

Number of views

98 (12 by ULiège)

Number of downloads

5 (5 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

Bibliography

Ewins, D.J., Modal Testing: Theory, Practice, and Application. second ed., 2000, Research Studies Press, Baldock, Hertfordshire, England, Philadelphia, PA.
Kerschen, G., Worden, K., Vakakis, A.F., Golinval, J.C., Past, present and future of nonlinear system identification in structural dynamics. Mech. Syst. Signal Process. 20:3 (2006), 505–592.
Vakakis, A.F., Manevitch, L.I., Mikhlin, Y.V., Pilipchuk, V.N., Zevin, A.A., Normal Modes and Localization in Nonlinear Systems. 1996, John Wiley & Sons, New York.
Rosenberg, R.M., Normal modes of nonlinear dual-mode systems. J. Appl. Mech. Trans. ASME 27:2 (1960), 263–268.
Rosenberg, R.M., The normal modes of nonlinear n-degree-of-freedom systems. J. Appl. Mech. 29:1 (1962), 7–14.
Kerschen, G., Peeters, M., Golinval, J.C., Vakakis, A.F., Nonlinear normal modes, Part I: A useful framework for the structural dynamicist. Mech. Syst. Signal Process. 23:1 (2009), 170–194.
Krack, M., Nonlinear modal analysis of nonconservative systems: Extension of the periodic motion concept. Comput. Struct. 154 (2015), 59–71.
Shaw, S.W., Pierre, C., Non-linear normal modes and invariant manifolds. J. Sound Vib. 150:1 (1991), 170–173.
Shaw, S.W., Pierre, C., Normal modes for non-linear vibratory systems. J. Sound Vib. 164:1 (1993), 85–124.
Haller, G., Ponsioen, S., Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction. Nonlinear Dynam. 86:3 (2016), 1493–1534.
Nayfeh, A.H., Mook, D.T., Nonlinear Oscillations. 1995, John Wiley & Sons, New York.
Guckenheimer, J., Holmes, P.J., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. 1983, Springer.
Vakakis, A.F., Blanchard, A., Exact steady states of the periodically forced and damped duffing oscillator. J. Sound Vib. 413 (2018), 57–65.
Hill, T.L., Cammarano, A., Neild, S.A., Wagg, D.J., Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves. J. Sound Vib. 349 (2015), 276–288.
Cenedese, M., Haller, G., How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proc. R. Soc. A Math. Phys. Eng. Sci., 476(2234), 2020, 20190494.
Hill, T.L., Cammarano, A., Neild, S.A., Barton, D.A., Identifying the significance of nonlinear normal modes. Proc. R. Soc. A Math. Phys. Eng. Sci., 473(2199), 2017, 20160789.
Géradin, M., Rixen, D., Mechanical Vibrations: Theory and Application to Structural Dynamics. third ed., 2015, John Wiley & Sons, New York.
Wright, J.R., Cooper, J.E., Desforges, M.J., Normal-mode force appropriation - theory and application. Mech. Syst. Signal Process. 13:2 (1999), 217–240.
Göge, D., Böswald, M., Füllekrug, U., Lubrina, P., Ground vibration testing of large aircraft - State-of-the-art and future perspectives. Conf. Proc. Soc. Exp. Mech. Ser., 2007, 2775–2787.
Atkins, P.A., Wright, J.R., Worden, K., An extenstion of force appropriation to the identification of non-linear multi-degree of freedom systems. J. Sound Vib. 237:1 (2000), 23–43.
Peeters, M., Kerschen, G., Golinval, J.C., Dynamic testing of nonlinear vibrating structures using nonlinear normal modes. J. Sound Vib. 330:3 (2011), 486–509.
Peeters, M., Kerschen, G., Golinval, J.C., Modal testing of nonlinear vibrating structures based on nonlinear normal modes: Experimental demonstration. Mech. Syst. Signal Process. 25:4 (2011), 1227–1247.
Noel, J.P., Renson, L., Grappasonni, C., Kerschen, G., Identification of nonlinear normal modes of engineering structures under broadband forcing. Mech. Syst. Signal Process. 74 (2016), 95–110.
Szalai, R., Ehrhardt, D., Haller, G., Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations. Proc. R. Soc. A Math. Phys. Eng. Sci., 473(2202), 2017, 20160759.
Renson, L., Gonzalez-Buelga, A., Barton, D.A., Neild, S.A., Robust identification of backbone curves using control-based continuation. J. Sound Vib. 367 (2016), 145–158.
Denis, V., Jossic, M., Giraud-Audinec, C., Chomette, B., Thomas, O., Identication of nonlinear modes using phase-locked-loop experimental continuation and normal form. Mech. Syst. Signal Process. 106 (2018), 430–452.
Scheel, M., Peter, S., Leine, R.I., Krack, M., A phase resonance approach for modal testing of structures with nonlinear dissipation. J. Sound Vib. 435 (2018), 56–73.
Renson, L., Hill, T.L., Ehrhardt, D.A., Barton, D.A., Neild, S.A., Force appropriation of nonlinear structures. Proc. R. Soc. A Math. Phys. Eng. Sci., 474(2214), 2018, 20170880.
Ehrhardt, D.A., Allen, M.S., Measurement of nonlinear normal modes using multi-harmonic stepped force appropriation and free decay. Mech. Syst. Signal Process. 76–77 (2016), 612–633.
Peeters, M., Viguié, R., Sérandour, G., Kerschen, G., Golinval, J.C., Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques. Mech. Syst. Signal Process. 23:1 (2009), 195–216.
Stoker, J.J., Nonlinear Vibrations in Mechanical and Electrical Systems. 1995, Interscience Publishers, New York.
Marchionne, A., Ditlevsen, P., Wieczorek, S., Synchronisation vs. resonance: Isolated resonances in damped nonlinear oscillators. Physica D 380–381 (2018), 8–16.
Yagasaki, K., Higher-order averaging and ultra-subharmonics in forced oscillators. J. Sound Vib. 210:4 (1998), 529–553.
Yagasaki, K., Detection of bifurcation structures by higher-order averaging for Duffing's equation. Nonlinear Dynam. 18:2 (1999), 129–158.
Leung, A.Y., Fung, T.C., Phase increment analysis of damped Duffing oscillators. Internat. J. Numer. Methods Engrg. 28:1 (1989), 193–209.
Parlitz, U., Lauterborn, W., Superstructure in the bifurcation set of the Duffing equation ẍ+dẋ+x+x3=fcos(ωt). Phys. Lett. A 107:8 (1985), 351–355.
Guillot, L., Lazarus, A., Thomas, O., Vergez, C., Cochelin, B., A purely frequency based floquet-hill formulation for the efficient stability computation of periodic solutions of ordinary differential systems. J. Comput. Phys., 416, 2020, 109477.
Babitsky, V.I., Autoresonant mechatronic systems. Mechatronics 5:5 (1995), 483–495.
Sokolov, I., Babitsky, V., Phase control of self-sustained vibration. J. Sound Vib. 248 (2001), 725–744.
Hill, T.L., Neild, S.A., Cammarano, A., An analytical approach for detecting isolated periodic solution branches in weakly nonlinear structures. J. Sound Vib. 379 (2016), 150–165.
Detroux, T., Renson, L., Masset, L., Kerschen, G., The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems. Comput. Methods Appl. Mech. Engrg. 296 (2015), 18–38.