Nonlinear vibrations and chaos in gongs and cymbals.

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Chaigne, Antoine et Touzé, Cyril et Thomas, Olivier (2005) Nonlinear vibrations and chaos in gongs and cymbals. Acoustical Science and Technology, 26 (5). pp. 403-409. ISSN 1346-3969

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URL officielle: http://www.jstage.jst.go.jp/article/ast/26/5/26_403/_article

Résumé

This paper summarizes some results obtained in the last few years for the modeling of nonlinear vibrating instruments such as gongs and cymbals. Linear, weakly nonlinear and chaotic regimes are successively examined. A theoretical mechanical model is presented, based on the nonlinear von Kármán equations for thin shallow spherical shells. Modal projection and Nonlinear Normal Mode (NNM) formulation leads to a subset of coupled nonlinear oscillators. Current developments are aimed at using this subset for sound synthesis purpose.

Références Bibliographiques

[1] T. D. Rossing, Science of Percussion Instruments (World

Scientific, Singapore, 2000).

[2] N. H. Fletcher, ‘‘The nonlinear physics of musical instruments,’’

Rep. Prog. Phys., 62, 723–764 (1999).

[3] C. Touze´ and A. Chaigne, ‘‘Lyapunov exponents from

experimental time series: application to cymbal vibrations,’’

Acustica - Acta Acustica, 86, 557–567 (2000).

[4] N. H. Fletcher, ‘‘Nonlinear frequency shifts in quasi-sphericalcaps

shells: Pitch glide in Chinese gongs,’’ J. Acoust. Soc. Am.,

78, 2069–2073 (1985).

[5] K. A. Legge and N. H. Fletcher, ‘‘Nonlinearity, chaos, and the

sound of shallow gongs,’’ J. Acoust. Soc. Am., 86, 2439–2443

(1989).

[6] A. Chaigne, C. Touze´ and O. Thomas, ‘‘Nonlinear axisymmetric

vibrations of gongs,’’ Proc. Int. Symp. Mus. Acoust.,

Perugia, Vol. 1, pp. 147–152 (2001).

[7] A. Chaigne, M. Fontaine, O. Thomas, M. Ferre´ and C. Touze´,

‘‘Vibrations of shallow spherical shells and gongs: A comparative

study,’’ Proc. Forum Acusticum, Sevilla, Mus-06-006-

IP (2002).

[8] O. Thomas, C. Touze´ and A. Chaigne, ‘‘Nonlinear vibrations of

free-edge thin spherical shells: modal interaction rules and

1:1:2 internal resonance,’’ Int. J. Solids Struct., 42, 3339–3373 (2005).

[9] O. Thomas, E. Luminais and C. Touze´, ‘‘Nonlinear modal

interactions in free-edge thin spherical shells: Measurements of

a 1:1:2 internal resonance,’’ 3rd MIT Conf. Computational

Fluid and Solid Mechanics, Boston (2005).

[10] O. Thomas, C. Touze´ and A. Chaigne, ‘‘Asymmetric non-linear

forced vibrations of free-edge circular plates, Part II: experiments,’’

J. Sound Vib., 265, 1075–1101 (2003).

[11] C. Touze´, O. Thomas and A. Chaigne, ‘‘Hardening-softening

behaviour in non-linear oscillations of structural systems using

nonlinear normal modes,’’ J. Sound Vib., 273, 77–101 (2004).

[12] A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations (Wiley,

New York, 1979).

[13] O. Thomas, C. Touze´ and A. Chaigne, ‘‘Non-linear behaviour

of gongs through the dynamics of simple rods systems,’’ Proc.

Int. Symp. Mus. Acoust., Perugia (2001).

[14] C. Touze´ and O. Thomas, ‘‘Nonlinear behavior of free-edge

shallow spherical shells: Effect of the geometry,’’ Int. J.

Nonlinear Mech. (submitted).

[15] T. D. Rossing and N. H. Fletcher, ‘‘Nonlinear vibrations in

plates and gongs,’’ J. Acoust. Soc. Am., 73, 345–351 (1983).

[16] N. Boivin, C. Pierre and S. W. Shaw, ‘‘Nonlinear normal

modes, invariance and modal dynamics approximations of

nonlinear systems,’’ Nonlinear Dyn., 8, 315–346 (1995).

[17] H. Kantz and T. Schreiber, Nonlinear Time Series Analysis,

Cambridge Nonlinear Sciences Series, Vol. 7 (Cambridge

University Press, Cambridge, 1997).

[18] P. Grassberger and I. Procaccia, ‘‘Measuring the strangeness of

strange attractors,’’ Physica D, 9, 189–208 (1983).

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