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Volumn 46, Issue 1, 2011, Pages 234-246

Transition to chaotic vibrations for harmonically forced perfect and imperfect circular plates

Author keywords

Bifurcation; Chaotic vibrations; Imperfect plates

Indexed keywords

BIFURCATION; BIFURCATION DIAGRAM; BIFURCATION SCENARIO; CHAOTIC STATE; CHAOTIC VIBRATION; CIRCULAR PLATES; CONSTANT FREQUENCY; CRITICAL FORCE; DIRECT TRANSITION; EIGEN FREQUENCIES; EIGEN MODES; ENERGY EXCHANGES; EXCITATION FREQUENCY; EXPERIMENTAL OBSERVATION; FOURIER SPECTRA; FREQUENCY RANGES; GALERKIN APPROACH; GEOMETRIC NON-LINEARITY; HARMONIC FORCING; HIGH-DIMENSIONAL CHAOS; IMPERFECT PLATES; INTERNAL RESONANCE; LARGE-AMPLITUDE VIBRATION; LYAPUNOV EXPONENT; POINCAR MAP; QUASI-PERIODIC; RESONANT MODE; THIN PLATE; WAVE TURBULENCE;

EID: 78649630932     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2010.09.004     Document Type: Article
Times cited : (56)

References (56)
  • 3
    • 0022349593 scopus 로고
    • Non-linear frequency shifts in quasispherical-cap shells: Pitch glide in chinese gongs
    • N.H. Fletcher Non-linear frequency shifts in quasispherical-cap shells: pitch glide in chinese gongs Journal of the Acoustical Society of America 78 6 1985 2069 2071
    • (1985) Journal of the Acoustical Society of America , vol.78 , Issue.6 , pp. 2069-2071
    • Fletcher, N.H.1
  • 7
    • 0039252495 scopus 로고    scopus 로고
    • Lyapunov exponents from experimental time series: Application to cymbal vibrations
    • C. Touz, and A. Chaigne Lyapunov exponents from experimental time series: application to cymbal vibrations Acta Acustica 86 3 2000 557 567
    • (2000) Acta Acustica , vol.86 , Issue.3 , pp. 557-567
    • Touz, C.1    Chaigne, A.2
  • 11
    • 78649633440 scopus 로고    scopus 로고
    • Analyse et modélisation de signaux acoustiques et vibratoires chaotiques
    • Ph.D. Thesis, Université Pierre et Marie Curie, Paris VI
    • C. Touz, Analyse et modlisation de signaux acoustiques et vibratoires chaotiques. application aux intruments de percussion non-linaires, Ph.D. Thesis, Universit Pierre et Marie Curie, Paris VI, 2000.
    • (2000) Application Aux Intruments de Percussion Non-linéaires
    • Touzé, C.1
  • 14
    • 0042346289 scopus 로고    scopus 로고
    • Bifurcations of a thin plate-strip excited transversally and axially
    • J. Awrejcewicz, V.A. Krysko, and G. Narkaitis Bifurcations of a thin plate-strip excited transversally and axially Nonlinear Dynamics 32 2003 187 209
    • (2003) Nonlinear Dynamics , vol.32 , pp. 187-209
    • Awrejcewicz, J.1    Krysko, V.A.2    Narkaitis, G.3
  • 17
    • 29344469052 scopus 로고    scopus 로고
    • Chaotic vibrations of circular cylindrical shells: Galerkin versus reduced-order models via the proper orthogonal decomposition method
    • M. Amabili, A. Sarkar, and M.P. Padoussis Chaotic vibrations of circular cylindrical shells: Galerkin versus reduced-order models via the proper orthogonal decomposition method Journal of Sound and Vibration 290 35 2006 736 762
    • (2006) Journal of Sound and Vibration , vol.290 , Issue.35 , pp. 736-762
    • Amabili, M.1    Sarkar, A.2    Padoussis, M.P.3
  • 18
    • 13544250560 scopus 로고    scopus 로고
    • Non-linear vibrations of doubly-curved shallow shells
    • M. Amabili Non-linear vibrations of doubly-curved shallow shells International Journal of Non-linear Mechanics 40 5 2005 683 710
    • (2005) International Journal of Non-linear Mechanics , vol.40 , Issue.5 , pp. 683-710
    • Amabili, M.1
  • 19
    • 33644952549 scopus 로고    scopus 로고
    • Dynamic instability and chaos of empty and fluid-filled circular cylindrical shells under periodic axial loads
    • F. Pellicano, and M. Amabili Dynamic instability and chaos of empty and fluid-filled circular cylindrical shells under periodic axial loads Journal of Sound and Vibration 293 12 2006 227 252
    • (2006) Journal of Sound and Vibration , vol.293 , Issue.12 , pp. 227-252
    • Pellicano, F.1    Amabili, M.2
  • 20
    • 0030257425 scopus 로고    scopus 로고
    • Characterizing the dynamic response of a thermally loaded, acoustically excited plate
    • K.D. Murphy, L.N. Virgin, and S.A. Rizzi Characterizing the dynamic response of a thermally loaded, acoustically excited plate Journal of Sound and Vibration 196 5 1996 635 658
    • (1996) Journal of Sound and Vibration , vol.196 , Issue.5 , pp. 635-658
    • Murphy, K.D.1    Virgin, L.N.2    Rizzi, S.A.3
  • 21
    • 10044291598 scopus 로고    scopus 로고
    • Chaotic oscillations of a shallow cylindrical shell with a concentrated mass under periodic excitation
    • K. Nagai, S. Maruyama, M. Oya, and T. Yamaguchi Chaotic oscillations of a shallow cylindrical shell with a concentrated mass under periodic excitation Computers and Structures 82 2004 2607 2619
    • (2004) Computers and Structures , vol.82 , pp. 2607-2619
    • Nagai, K.1    Maruyama, S.2    Oya, M.3    Yamaguchi, T.4
  • 22
    • 34447539648 scopus 로고    scopus 로고
    • Experiments and analysis on chaotic vibrations of a shallow cylindrical shell-panel
    • K. Nagai, S. Maruyama, T. Murata, and T. Yamaguchi Experiments and analysis on chaotic vibrations of a shallow cylindrical shell-panel Journal of Sound and Vibration 305 2007 492 520
    • (2007) Journal of Sound and Vibration , vol.305 , pp. 492-520
    • Nagai, K.1    Maruyama, S.2    Murata, T.3    Yamaguchi, T.4
  • 23
    • 44649102566 scopus 로고    scopus 로고
    • Modal interactions in chaotic vibrations of a shallow double-curved shell-panel
    • S. Maruyama, K. Nagai, and Y. Tsuruta Modal interactions in chaotic vibrations of a shallow double-curved shell-panel Journal of Sound and Vibration 315 2008 607 625
    • (2008) Journal of Sound and Vibration , vol.315 , pp. 607-625
    • Maruyama, S.1    Nagai, K.2    Tsuruta, Y.3
  • 24
    • 0346939177 scopus 로고    scopus 로고
    • Finite dimensionality of an attractor in some problems of nonlinear shell theory
    • I. Chueshov Finite dimensionality of an attractor in some problems of nonlinear shell theory Mathematics of the USSR Sbornik 61 2 1998 411 420
    • (1998) Mathematics of the USSR Sbornik , vol.61 , Issue.2 , pp. 411-420
    • Chueshov, I.1
  • 25
    • 0001654129 scopus 로고
    • Finite-dimensionality of attractors associated with von Krmn plate equations and boundary damping
    • I. Lasiecka Finite-dimensionality of attractors associated with von Krmn plate equations and boundary damping Journal of Differential Equations 117 1995 357 389
    • (1995) Journal of Differential Equations , vol.117 , pp. 357-389
    • Lasiecka, I.1
  • 27
    • 1542406498 scopus 로고    scopus 로고
    • Global attractors for von Krmn evolutions with a nonlinear boundary dissipation
    • I. Chueshov, and I. Lasiecka Global attractors for von Krmn evolutions with a nonlinear boundary dissipation Journal of Differential Equations 198 2004 196 231
    • (2004) Journal of Differential Equations , vol.198 , pp. 196-231
    • Chueshov, I.1    Lasiecka, I.2
  • 28
    • 51849118403 scopus 로고    scopus 로고
    • Attractors and long time behavior of von Krmn thermoelastic plates
    • I. Chueshov, and I. Lasiecka Attractors and long time behavior of von Krmn thermoelastic plates Applied Mathematics and Optimization 58 2008 195 241
    • (2008) Applied Mathematics and Optimization , vol.58 , pp. 195-241
    • Chueshov, I.1    Lasiecka, I.2
  • 30
    • 0035873762 scopus 로고    scopus 로고
    • Wave turbulence and intermittency
    • A. Newell, S. Nazarenko, and L. Biven Wave turbulence and intermittency Physica D 152153 2001 520 550
    • (2001) Physica D , vol.152-153 , pp. 520-550
    • Newell, A.1    Nazarenko, S.2    Biven, L.3
  • 31
    • 33749044987 scopus 로고    scopus 로고
    • Weak turbulence for a vibrating plate: Can one hear a Kolmogorov spectrum?
    • G. Dring, C. Josserand, and S. Rica Weak turbulence for a vibrating plate: can one hear a Kolmogorov spectrum? Physical Review Letters 97 2006 025503
    • (2006) Physical Review Letters , vol.97 , pp. 025503
    • Dring, G.1    Josserand, C.2    Rica, S.3
  • 33
    • 57849120395 scopus 로고    scopus 로고
    • Statistics of power injection in a plate set into chaotic vibration
    • O. Cadot, A. Boudaoud, and C. Touz Statistics of power injection in a plate set into chaotic vibration European Physics Journal B 66 2008 399 407
    • (2008) European Physics Journal B , vol.66 , pp. 399-407
    • Cadot, O.1    Boudaoud, A.2    Touz, C.3
  • 34
    • 45249088575 scopus 로고    scopus 로고
    • Are there waves in elastic wave turbulence?
    • N. Mordant Are there waves in elastic wave turbulence? Physical Review Letters 100 2008 234505
    • (2008) Physical Review Letters , vol.100 , pp. 234505
    • Mordant, N.1
  • 35
    • 85143679579 scopus 로고
    • Influence of large amplitudes on free flexural vibrations of rectangular elastic plates
    • H.-N. Chu, and G. Herrmann Influence of large amplitudes on free flexural vibrations of rectangular elastic plates Journal of Applied Mechanics 23 1956 532 540
    • (1956) Journal of Applied Mechanics , vol.23 , pp. 532-540
    • Chu, H.-N.1    Herrmann, G.2
  • 37
    • 60549117670 scopus 로고    scopus 로고
    • Non-linear vibrations of imperfect free-edge circular plates and shells
    • C. Camier, C. Touz, and O. Thomas Non-linear vibrations of imperfect free-edge circular plates and shells European Journal of Mechanics A/Solids 28 2009 500 515
    • (2009) European Journal of Mechanics A/Solids , vol.28 , pp. 500-515
    • Camier, C.1    Touz, C.2    Thomas, O.3
  • 38
    • 0001258001 scopus 로고
    • Effects of initial imperfections on dynamic behaviour of rectangular plates
    • G. Ostiguy, and S. Sassi Effects of initial imperfections on dynamic behaviour of rectangular plates Non-linear Dynamics 3 1992 165 181
    • (1992) Non-linear Dynamics , vol.3 , pp. 165-181
    • Ostiguy, G.1    Sassi, S.2
  • 39
    • 31644431511 scopus 로고    scopus 로고
    • Theory and experiments for large-amplitude vibrations of rectangular plates with geometric imperfections
    • DOI 10.1016/j.jsv.2005.06.007, PII S0022460X05003974
    • M. Amabili Theory and experiments for large-amplitude vibrations of rectangular plates with geometric imperfections Journal of Sound and Vibration 291 35 2006 539 565 (Pubitemid 43172066)
    • (2006) Journal of Sound and Vibration , vol.291 , Issue.3-5 , pp. 539-565
    • Amabili, M.1
  • 40
    • 0042816749 scopus 로고    scopus 로고
    • Asymmetric non-linear forced vibrations of free-edge circular plates, part I: Theory
    • C. Touz, O. Thomas, and A. Chaigne Asymmetric non-linear forced vibrations of free-edge circular plates, part I: theory Journal of Sound and Vibration 258 4 2002 649 676
    • (2002) Journal of Sound and Vibration , vol.258 , Issue.4 , pp. 649-676
    • Touz, C.1    Thomas, O.2    Chaigne, A.3
  • 41
    • 13444303912 scopus 로고    scopus 로고
    • Non-linear vibrations of free-edge thin spherical shells: Modal interaction rules and 1:1:2 internal resonance
    • O. Thomas, C. Touz, and A. Chaigne Non-linear vibrations of free-edge thin spherical shells: modal interaction rules and 1:1:2 internal resonance International Journal of Solids and Structures 42 1112 2005 3339 3373
    • (2005) International Journal of Solids and Structures , vol.42 , Issue.1112 , pp. 3339-3373
    • Thomas, O.1    Touz, C.2    Chaigne, A.3
  • 42
    • 0000893170 scopus 로고    scopus 로고
    • Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid, part I: Stability
    • M. Amabili, F. Pellicano, and M.P. Padoussis Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid, part I: stability Journal of Sound and Vibration 225 4 1999 655 699
    • (1999) Journal of Sound and Vibration , vol.225 , Issue.4 , pp. 655-699
    • Amabili, M.1    Pellicano, F.2    Padoussis, M.P.3
  • 43
    • 0034320007 scopus 로고    scopus 로고
    • Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part III: Truncation effect without flow and experiments
    • DOI 10.1006/jsvi.2000.3071
    • M. Amabili, F. Pellicano, and M.P. Padoussis Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid, part III: truncation effect without flow and experiments Journal of Sound and Vibration 237 4 2000 617 640 (Pubitemid 32017903)
    • (2000) Journal of Sound and Vibration , vol.237 , Issue.4 , pp. 617-640
    • Amabili, M.1    Pellicano, F.2    Paidoussis, M.P.3
  • 44
    • 33745891539 scopus 로고    scopus 로고
    • Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry
    • C. Touz, and O. Thomas Non-linear behaviour of free-edge shallow spherical shells: effect of the geometry International Journal of Non-linear Mechanics 41 5 2006 678 692
    • (2006) International Journal of Non-linear Mechanics , vol.41 , Issue.5 , pp. 678-692
    • Touz, C.1    Thomas, O.2
  • 49
    • 2342517458 scopus 로고    scopus 로고
    • Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes
    • C. Touz, O. Thomas, and A. Chaigne Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes Journal of Sound and Vibration 273 12 2004 77 101
    • (2004) Journal of Sound and Vibration , vol.273 , Issue.12 , pp. 77-101
    • Touz, C.1    Thomas, O.2    Chaigne, A.3
  • 50
    • 34248373279 scopus 로고    scopus 로고
    • Non-linear vibrations of free-edge thin spherical shells: Experiments on a 1:1:2 internal resonance
    • O. Thomas, C. Touz, and E. Luminais Non-linear vibrations of free-edge thin spherical shells: experiments on a 1:1:2 internal resonance Nonlinear Dynamics 49 12 2007 259 284
    • (2007) Nonlinear Dynamics , vol.49 , Issue.12 , pp. 259-284
    • Thomas, O.1    Touz, C.2    Luminais, E.3
  • 52
    • 0003686037 scopus 로고    scopus 로고
    • Nonlinear Interactions: Analytical, Computational and Experimental Methods
    • New York
    • A.H. Nayfeh, Nonlinear Interactions: Analytical, Computational and Experimental Methods, Wiley Series in Nonlinear Science, New York, 2000.
    • (2000) Wiley Series in Nonlinear Science
    • Nayfeh, A.H.1
  • 53
    • 48749145669 scopus 로고
    • The dimension of chaotic attractors
    • J. Farmer, E. Ott, and J. Yorke The dimension of chaotic attractors Physica D 7 13 1983 153 180
    • (1983) Physica D , vol.7 , Issue.13 , pp. 153-180
    • Farmer, J.1    Ott, E.2    Yorke, J.3
  • 54
    • 0001727830 scopus 로고
    • Symmetry property of the Lyapunov spectra of a class of dissipative dynamical systems with viscous damping
    • U. Dressler Symmetry property of the Lyapunov spectra of a class of dissipative dynamical systems with viscous damping Physical Review A 38 4 1988 2103 2109
    • (1988) Physical Review A , vol.38 , Issue.4 , pp. 2103-2109
    • Dressler, U.1
  • 55
    • 47649103125 scopus 로고    scopus 로고
    • Effect of imperfections and damping on the type of non-linearity of circular plates and shallow spherical shells
    • Article ID 678307
    • C. Touz, C. Camier, G. Favraud, O. Thomas, Effect of imperfections and damping on the type of non-linearity of circular plates and shallow spherical shells, Mathematical Problems in Engineering 2008 (2008) Article ID 678307.
    • (2008) Mathematical Problems in Engineering 2008
    • C. Touzé1


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