Nonlinear vibration localisation in a symmetric system of two coupled beams

Fontanela, Filipe; Vizzaccaro, Alessandra; Auvray, Jeanne; Niedergesäß, Björn; Grolet, Aurélien; Salles, Loïc; Hoffmann, Norbert

doi:10.1007/s11071-020-05760-x

Download

Article (Scientific journals)

Nonlinear vibration localisation in a symmetric system of two coupled beams

Fontanela, Filipe; Vizzaccaro, Alessandra; Auvray, Jeanne et al.

2021 • In Nonlinear Dynamics, 103 (4), p. 3417 - 3428

Peer reviewed

Permalink
https://hdl.handle.net/2268/334064

DOI
10.1007/s11071-020-05760-x

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

fontanela-NLDyn2021.pdf

Publisher postprint (3.28 MB)

Download

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Vibration localisation; Symmetry breaking bifurcation; Clearance nonlinearity

Abstract :

[en] We report nonlinear vibration localisation in a system of two symmetric weakly coupled nonlinear oscillators. A two degree-of-freedom model with piecewise linear stiffness shows bifurcations to localised solutions. An experimental investigation employing two weakly coupled beams touching against stoppers for large vibration amplitudes confirms the nonlinear localisation.

Disciplines :

Mechanical engineering

Author, co-author :

Fontanela, Filipe

Vizzaccaro, Alessandra

Auvray, Jeanne

Niedergesäß, Björn

Grolet, Aurélien

Salles, Loïc ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Vibration of Turbomachines ; Imperial College London > Mechanical Engineering > Vibration University Technology Center

Hoffmann, Norbert

Language :

English

Title :

Nonlinear vibration localisation in a symmetric system of two coupled beams

Publication date :

2021

Journal title :

Nonlinear Dynamics

ISSN :

0924-090X

eISSN :

1573-269X

Volume :

103

Issue :

Pages :

3417 - 3428

Peer reviewed :

Peer reviewed

Available on ORBi :

since 06 July 2025

Statistics

Number of views

12 (0 by ULiège)

Number of downloads

11 (0 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Bendiksen, O.: Localization phenomena in structural dynamics. Chaos Solitons Fractals 11(10), 1621–1660 (2000) DOI: 10.1016/S0960-0779(00)00013-8
Bendiksen, O.O.: Mode localization phenomena in large space structures. AIAA J. 25(9), 1241–1248 (1987) DOI: 10.2514/3.9773
Capiez-Lernout, E., Soize, C., Mbaye, M.: Mistuning analysis and uncertainty quantification of an industrial bladed disk with geometrical nonlinearity. J. Sound Vib. 356, 124–143 (2015) DOI: 10.1016/j.jsv.2015.07.006
Castanier, M.P., Pierre, C.: Modeling and analysis of mistuned bladed disk vibration: current status and emerging directions. J. Propuls. Power 22(2), 384–396 (2006) DOI: 10.2514/1.16345
Champneys, A.R., Kuznetsov, Y.A., Sandstede, B.: A numerical toolbox for homoclinic bifurcation analysis. Int. J. Bifurc. Chaos 6(05), 867–887 (1996) DOI: 10.1142/S0218127496000485
Cornwell, P.J., Bendiksen, O.O.: Localization of vibrations in large space reflectors. AIAA J. 27(2), 219–226 (1989) DOI: 10.2514/3.10084
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. Eng. 296, 18–38 (2015) DOI: 10.1016/j.cma.2015.07.017
Doedel, E.J., Champneys, A.R., Fairgrieve, T.F., Kuznetsov, Y.A., Sandstede, B., Wang, X., et al.: Auto97. Continuation and bifurcation software for ordinary differential equations (1998)
Emaci, E., Nayfeh, T.A., Vakakis, A.F.: Numerical and experimental study of nonlinear localization in a flexible structure with vibro-impacts. ZAMM. Z. Angew. Math. Mech. 77(7), 527–541 (1997). 10.1002/zamm.19970770712 DOI: 10.1002/zamm.19970770712
Flach, S., Gorbach, A.V.: Discrete breathersadvances in theory and applications. Phys. Rep. 467(1–3), 1–116 (2008) DOI: 10.1016/j.physrep.2008.05.002
Flach, S., Willis, C.R.: Discrete breathers. Phys. Rep. 295(5), 181–264 (1998) DOI: 10.1016/S0370-1573(97)00068-9
Hill, T., Cammarano, A., Neild, S., Wagg, D.: Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves. J. Sound Vib. 349, 276–288 (2015). 10.1016/j.jsv.2015.03.030 DOI: 10.1016/j.jsv.2015.03.030
Hodges, C.: Confinement of vibration by structural irregularity. J. Sound Vib. 82(3), 411–424 (1982) DOI: 10.1016/S0022-460X(82)80022-9
Hodges, C., Woodhouse, J.: Vibration isolation from irregularity in a nearly periodic structure: theory and measurements. J. Acoust. Soc. Am. 74(3), 894–905 (1983) DOI: 10.1121/1.389847
Ikeda, T., Harata, Y., Nishimura, K.: Intrinsic localized modes of harmonic oscillations in nonlinear oscillator arrays. J. Comput. Nonlinear Dyn. 8(4), 041009 (2013). 10.1115/1.4023866 DOI: 10.1115/1.4023866
Judge, J., Pierre, C., Mehmed, O.: Experimental investigation of mode localization and forced response amplitude magnification for a mistuned bladed disk. J. Eng. Gas Turbines Power 123(4), 940–950 (2000) DOI: 10.1115/1.1377872
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), 170–194 (2009) DOI: 10.1016/j.ymssp.2008.04.002
Krack, M., Salles, L., Thouverez, F.: Vibration prediction of bladed disks coupled by friction joints. Arch. Comput. Methods Eng. 24(3), 589–636 (2017) DOI: 10.1007/s11831-016-9183-2
Papangelo, A., Fontanela, F., Grolet, A., Ciavarella, M., Hoffmann, N.: Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled duffing oscillators. J. Sound Vib. 440, 202–211 (2019) DOI: 10.1016/j.jsv.2018.10.028
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), 195–216 (2009) DOI: 10.1016/j.ymssp.2008.04.003
Rebouas, G.F.S., Santos, I.F., Thomsen, J.J.: Validation of vibro-impact force models by numerical simulation, perturbation methods and experiments. J. Sound Vib. 413, 291–307 (2018). 10.1016/j.jsv.2017.10.028 DOI: 10.1016/j.jsv.2017.10.028
Sato, M., Hubbard, B., Sievers, A., Ilic, B., Czaplewski, D., Craighead, H.: Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array. Phys. Rev. Lett. 90(4), 044102 (2003) DOI: 10.1103/PhysRevLett.90.044102
Vakakis, A.F.: Dynamics of a nonlinear periodic structure with cyclic symmetry. Acta Mech. 95(1–4), 197–226 (1992) DOI: 10.1007/BF01170813
Vargiu, P., Firrone, C., Zucca, S., Gola, M.: A reduced order model based on sector mistuning for the dynamic analysis of mistuned bladed disks. Int. J. Mech. Sci. 53(8), 639–646 (2011) DOI: 10.1016/j.ijmecsci.2011.05.010
Whitehead, D.: Effect of mistuning on the vibration of turbo-machine blades induced by wakes. J. Mech. Eng. Sci. 8(1), 15–21 (1966) DOI: 10.1243/JMES_JOUR_1966_008_004_02