Nonlinear modes of clarinet-like musical instruments

Journal of Sound and Vibration

Volumn 324, Issue 3-5, 2009, Pages 983-1002

  Noreland, Daniel ^a   Bellizzi, Sergio ^a   Vergez, Christophe ^a   Bouc, Robert ^a  

^a LABORATOIRE DE MÉCANIQUE ET D ACOUSTIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC PRESSURES; AIR COLUMN; DAMPING FUNCTION; EXPLICIT INTEGRATION; INVARIANT MANIFOLDS; LIMIT CYCLE; MODAL EXPANSION; NONLINEAR MODE; NONLINEAR RELATIONS; NORMAL MODES; PHASE SPACES; PRESSURE DIFFERENCES; SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS; VOLUME FLOW; WOODWIND REEDS;

ACOUSTIC IMPEDANCE; DYNAMICAL SYSTEMS; MUSICAL INSTRUMENTS; NONLINEAR EQUATIONS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 67349212595     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2009.02.043     Document Type: Article

References (32)

1. Helmholtz H.L.F. On the Sensation of Tone (1877), Masson, Paris reprinted by Dover, from the first edition in 1954
2. Fletcher N.H., and Rossing T.D. The Physics of Musical Instruments (1991), Springer, Berlin
3. Rosenberg R. The normal modes of nonlinear n-degree-of-freedom systems. Journal of Applied Mechanics 29 (1962) 7-14
4. Shaw S., and Pierre C. Non-linear normal modes and invariant manifolds. Journal of Sound and Vibration 150 1 (1991) 170-173
5. Shaw S., and Pierre C. Normal modes for nonlinear vibratory systems. Journal of Sound and Vibration 164 1 (1993) 85-124
6. Pellicano F., and Mastroddi F. Applicability conditions of a nonlinear superposition technique. Journal of Sound and Vibration 200 1 (1997) 3-14
7. Jiang D., Pierre C., and Shaw S. Large-amplitude non-linear normal modes of piecewise linear systems. Journal of Sound and Vibration 272 3-5 (2004) 869-891
8. Jezequel L., and Lamarque C. Analysis of nonlinear dynamical systems by normal form theory. Journal of Sound and Vibration 149 3 (1991) 429-459
9. Nayfeh A. Method of Normal Forms (1993), Wiley, New York
10. Touzé C., Thomas O., and Chaigne A. Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes. Journal of Sound and Vibration 273 1-2 (2004) 77-101
11. Vakakis A. Nonlinear normal modes (NNMs) and their applications in vibration theory: an overview. Mechanical Systems and Signal Processing 11 1 (1997) 3-22
12. Vakakis A., Manevitch L., Mikhlin Y., Pilipchuk V., and Zevin A. Normal Modes and Localization in Nonlinear Systems (1996), Wiley Interscience, New York
13. Bellizzi S., and Bouc R. An amplitude phase formulation for nonlinear modes and limit cycles through invariant manifolds. Journal of Sound and Vibration 300 3-5 (2007) 896-915
14. Bellizzi S., and Bouc R. Analysis of multi-degree of freedom strongly non-linear mechanical systems with random input. Part I: non-linear modes and stochastic averaging. Probabilistic Engineering Mechanics 14 (1999) 229-244
15. Backus J. Small vibration theory of the clarinet. Journal of the Acoustical Society of America 35 (1963) 305
16. Nederveen C.J. Acoustical Aspects of Woodwind Instruments (1969), Fritz Knuf Publisher, Amsterdam
17. W.E. Worman, Self-sustained nonlinear oscillations of medium amplitude in clarinet-like systems, Ph.D. Thesis, Case Western Reserve University, 1971, Ann Arbor University Microfilms (ref. 71-22869).
18. Wilson T.A., and Beavers G.S. Operating modes of the clarinet. Journal of the Acoustical Society of America 56 (1974) 653
19. Schumacher R.T. Ab initio calculations of the oscillations of a clarinet. Acoustica 48 (1981) 71-85
20. A. Hirschberg, J. Gilbert, A.P.J. Wijnands, A.M.C. Valkering, Musical aero-acoustics of the clarinet, Journal de Physique IV 4 (1994) C5-559, C5-568, colloque C5 supplément au Journal de Physique III.
21. A. Hirschberg, Aero-acoustics of wind instruments, in: A. Hirschberg, J. Kergomard, G. Weinreich (Eds.), Mechanics of Musical Instruments, Springer, Berlin, 1995.
22. J. Kergomard, Elementary considerations on reed-instrument oscillations, in: A. Hirschberg, J. Kergomard, G. Weinreich (Eds.), Mechanics of Musical Instruments, Springer, Berlin, 1995.
23. Fritz C., Farner S., and Kergomard J. Some aspects of the harmonic balance method applied to the clarinet. Applied Acoustics 65 (2004) 1155-1180
24. V. Debut, Deux études d'un instrument de musique de type clarinette: analyse des fréquences propres du résonateur et calcul des auto-oscillations par décomposition modale (Two studies of a clarinet-like musical instrument: analysis of the eigen frequencies and calculation of the self-sustained oscillations by modal decomposition), Ph.D. Thesis, Aix-Marseille 2 university, 2004 〈http://tel.ccsd.cnrs.fr/tel-00008711〉.
25. Bellizzi S., and Bouc R. A new formulation for the existence and calculation of non-linear normal modes. Journal of Sound and Vibration 287 3 (2005) 545-569
26. Gottlieb D., and Orszag S.A. Numerical Analysis of Spectral Methods: Theory and Applications (1977), Society for Industrial and Applied Mathematics, Philadelphia, PA
27. Meirovitch L. Computational Methods in Structural Dynamics (1980), Sijthoff & Noordhoff, Alphen a/d Rijn
28. Arquier R., Bellizzi S., Bouc R., and Cochelin B. Two methods for the computation of nonlinear modes of vibrating systems at large amplitudes. Computer and Structures 84 (2006) 1565-1576
29. Hale J. Ordinary Differential Equations (1969), Wiley-Interscience, New York
30. Hairer E., and Wanner G. Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems (1996), Springer, Berlin
31. Gustafsson B., Kreiss H.O., and Oliger J. Time Dependent Problems and Difference Methods (1995), Wiley, New York
32. Pesheck E., Shaw S., and Pierre C. A new Galerkin-based approach for accurate nonlinear normal modes through invariant manifolds. Journal of Sound and Vibration 249 5 (2002) 971-993