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Volumn 14, Issue 3, 1997, Pages 211-229

Chaotic Dynamics of a Harmonically Excited Spring-Pendulum System with Internal Resonance

Author keywords

Chaos; Lyapunov exponent; Spring pendulum system

Indexed keywords

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); DEGREES OF FREEDOM (MECHANICS); LYAPUNOV METHODS; NONLINEAR SYSTEMS; PENDULUMS; RESONANCE; SPRINGS (COMPONENTS);

EID: 0031281218     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008256920441     Document Type: Article
Times cited : (69)

References (38)
  • 1
    • 0000106250 scopus 로고
    • Resonant motion of a spherical pendulum
    • Miles, J., 'Resonant motion of a spherical pendulum', Physica 11D, 1984, 309-323.
    • (1984) Physica , vol.11 D , pp. 309-323
    • Miles, J.1
  • 2
    • 0012212486 scopus 로고
    • Resonantly forced motion of two quadratically coupled oscillators
    • Miles, J., 'Resonantly forced motion of two quadratically coupled oscillators', Physica 13D, 1984, 247-260.
    • (1984) Physica , vol.13 D , pp. 247-260
    • Miles, J.1
  • 3
    • 0022078161 scopus 로고
    • Period-doubling bifurcations and modulated motions in forced mechanical systems
    • Tousi, S. and Bajaj, A. K., 'Period-doubling bifurcations and modulated motions in forced mechanical systems', ASME Journal of Applied Mechanics 52, 1985, 446-452.
    • (1985) ASME Journal of Applied Mechanics , vol.52 , pp. 446-452
    • Tousi, S.1    Bajaj, A.K.2
  • 4
    • 0022787327 scopus 로고
    • Chaos in a harmonically excited elastic beam
    • Maewal, A., 'Chaos in a harmonically excited elastic beam', ASME Journal of Applied Mechanics 53, 1986, 625-632.
    • (1986) ASME Journal of Applied Mechanics , vol.53 , pp. 625-632
    • Maewal, A.1
  • 5
    • 0023453251 scopus 로고
    • Parametric excitation of two internally resonant oscillators
    • Nayfeh, A. H., 'Parametric excitation of two internally resonant oscillators', Journal of Sound and Vibration 119(1), 1987, 95-109.
    • (1987) Journal of Sound and Vibration , vol.119 , Issue.1 , pp. 95-109
    • Nayfeh, A.H.1
  • 6
    • 0023407724 scopus 로고
    • Nonlinear forced response of infinitely long circular cylindrical shells
    • Nayfeh, A. H. and Raouf, R. A., 'Nonlinear forced response of infinitely long circular cylindrical shells', ASME Journal of Applied Mechanics 54, 1987, 571-577.
    • (1987) ASME Journal of Applied Mechanics , vol.54 , pp. 571-577
    • Nayfeh, A.H.1    Raouf, R.A.2
  • 7
    • 0026375666 scopus 로고
    • Nonlinear response of infinitely long circular cylindrical shells to subharmonic radial loads
    • Nayfeh, A. H., Raouf, R. A., and Nayfeh, J. F., 'Nonlinear response of infinitely long circular cylindrical shells to subharmonic radial loads', ASME Journal of Applied Mechanics 58, 1991, 1033-1041.
    • (1991) ASME Journal of Applied Mechanics , vol.58 , pp. 1033-1041
    • Nayfeh, A.H.1    Raouf, R.A.2    Nayfeh, J.F.3
  • 8
    • 0012131896 scopus 로고
    • Three-mode interactions in harmonically excited systems with quadratic nonlinearities
    • Nayfeh, T. A., Asrar, W., and Nayfeh, A. H., 'Three-mode interactions in harmonically excited systems with quadratic nonlinearities', Nonlinear Dynamics 3, 1992, 385-401.
    • (1992) Nonlinear Dynamics , vol.3 , pp. 385-401
    • Nayfeh, T.A.1    Asrar, W.2    Nayfeh, A.H.3
  • 9
    • 85024523123 scopus 로고
    • Modal interactions in dynamical and structural system
    • Nayfeh, A. H. and Balachandran, B., 'Modal interactions in dynamical and structural system', Applied Mechanics Review 42(11), part 2, 1989, s175-s210.
    • (1989) Applied Mechanics Review , vol.42 , Issue.11 PART 2
    • Nayfeh, A.H.1    Balachandran, B.2
  • 10
    • 0024069822 scopus 로고
    • Experimental observation of amplitude- and phase-modulated responses of two internally coupled oscillators to a harmonic excitation
    • Nayfeh, A. H. and Zavodney, L. D., 'Experimental observation of amplitude- and phase-modulated responses of two internally coupled oscillators to a harmonic excitation', ASME Journal of Applied Mechanics 55, 1988, 706-710.
    • (1988) ASME Journal of Applied Mechanics , vol.55 , pp. 706-710
    • Nayfeh, A.H.1    Zavodney, L.D.2
  • 11
    • 0024922153 scopus 로고
    • An experimental investigation of complicated responses of a two-degree-of freedom structure
    • Nayfeh, A. H., Balachandran, B., Colbert, M. A., and Nayfeh, M. A., 'An experimental investigation of complicated responses of a two-degree-of freedom structure', ASME Journal of Applied Mechanics 56, 1989, 960-967.
    • (1989) ASME Journal of Applied Mechanics , vol.56 , pp. 960-967
    • Nayfeh, A.H.1    Balachandran, B.2    Colbert, M.A.3    Nayfeh, M.A.4
  • 12
    • 0025536588 scopus 로고
    • Experimental investigation of resonantly forced oscillations of a two-degree-of-freedom structure
    • Nayfeh, A. H. and Balachandran, B., 'Experimental investigation of resonantly forced oscillations of a two-degree-of-freedom structure', International Journal of Non-Linear Mechanics 25(2/3), 1990, 199-209.
    • (1990) International Journal of Non-Linear Mechanics , vol.25 , Issue.2-3 , pp. 199-209
    • Nayfeh, A.H.1    Balachandran, B.2
  • 13
    • 0024964208 scopus 로고
    • Amplitude modulated and chaotic in resonance motion of strings
    • Johnson, J. M. and Bajaj, A. K., 'Amplitude modulated and chaotic in resonance motion of strings', Journal of Sound and Vibration 128(1), 1989, 87-107.
    • (1989) Journal of Sound and Vibration , vol.128 , Issue.1 , pp. 87-107
    • Johnson, J.M.1    Bajaj, A.K.2
  • 14
    • 0025539075 scopus 로고
    • Asymptotic techniques and complex dynamics in weakly nonlinear forced mechanical system
    • Bajaj, A. K. and Johnson, J. M., 'Asymptotic techniques and complex dynamics in weakly nonlinear forced mechanical system', International Journal of Non-Linear Mechanics 25(2/3), 1990, 211-226.
    • (1990) International Journal of Non-Linear Mechanics , vol.25 , Issue.2-3 , pp. 211-226
    • Bajaj, A.K.1    Johnson, J.M.2
  • 16
    • 0025550473 scopus 로고
    • Torus doublings and chaotic amplitude modulations in a two degree-of-freedom resonantly forced mechanical system
    • Bajaj, A. K. and Tousi, S., 'Torus doublings and chaotic amplitude modulations in a two degree-of-freedom resonantly forced mechanical system', International Journal of Non-Linear Mechanics 25(6), 1990, 625-641.
    • (1990) International Journal of Non-Linear Mechanics , vol.25 , Issue.6 , pp. 625-641
    • Bajaj, A.K.1    Tousi, S.2
  • 17
    • 0040521189 scopus 로고    scopus 로고
    • Chaotic responses in two degree-of-freedom systems with 1:2 internal resonances
    • Banerjee, B. and Bajaj, A. K., 'Chaotic responses in two degree-of-freedom systems with 1:2 internal resonances', Fields Institute Communications 9, 1996, 1-21.
    • (1996) Fields Institute Communications , vol.9 , pp. 1-21
    • Banerjee, B.1    Bajaj, A.K.2
  • 18
    • 0029771725 scopus 로고    scopus 로고
    • Resonant dynamics of an autoparametric system: A study using higher-order averaging
    • Banerjee, B., Bajaj, A. K., and Davies, P., 'Resonant dynamics of an autoparametric system: A study using higher-order averaging', International Journal of Non-Linear Mechanics 31, 1996, 21-39.
    • (1996) International Journal of Non-Linear Mechanics , vol.31 , pp. 21-39
    • Banerjee, B.1    Bajaj, A.K.2    Davies, P.3
  • 19
    • 0015672134 scopus 로고
    • Nonlinear coupling of pitch and roll modes in ship motions
    • Nayfeh, A. H., Mook, D. T., and Marshall, A. R., 'Nonlinear coupling of pitch and roll modes in ship motions', Journal of Hydronautics 7(4), 1973, 145-152.
    • (1973) Journal of Hydronautics , vol.7 , Issue.4 , pp. 145-152
    • Nayfeh, A.H.1    Mook, D.T.2    Marshall, A.R.3
  • 20
    • 0026817511 scopus 로고
    • Domains of attraction of system of nonlinearly coupled ship motions by simple cell mapping
    • Lee, W. K., 'Domains of attraction of system of nonlinearly coupled ship motions by simple cell mapping', ASME Journal of Offshore Mechanics and Arctic Engineering 114, 1992, 22-27.
    • (1992) ASME Journal of Offshore Mechanics and Arctic Engineering , vol.114 , pp. 22-27
    • Lee, W.K.1
  • 22
    • 84986998749 scopus 로고
    • On a class of two-degree-of-freedom oscillations
    • Kane, T. R. and Kahn, M. E., 'On a class of two-degree-of-freedom oscillations', ASME Journal of Applied Mechanics 35, 1968, 547-552.
    • (1968) ASME Journal of Applied Mechanics , vol.35 , pp. 547-552
    • Kane, T.R.1    Kahn, M.E.2
  • 23
    • 0041139407 scopus 로고
    • Periodic solutions of a spring pendulum system
    • Broucke, R. and Baxa, P. A., 'Periodic solutions of a spring pendulum system', Celestial Mechanics 8, 1973, 261-267.
    • (1973) Celestial Mechanics , vol.8 , pp. 261-267
    • Broucke, R.1    Baxa, P.A.2
  • 25
    • 0346548472 scopus 로고
    • Autoparametric self-excitation of a pendulum type elastic oscillator
    • Srinivasan, P. and Sankar, T. S., 'Autoparametric self-excitation of a pendulum type elastic oscillator', Journal of Sound and Vibration 35(4), 1974, 549-557.
    • (1974) Journal of Sound and Vibration , vol.35 , Issue.4 , pp. 549-557
    • Srinivasan, P.1    Sankar, T.S.2
  • 26
    • 2342494249 scopus 로고
    • On the asymptotic approximations of the solutions of a system of two non-linearly coupled harmonic oscillators
    • van der Burgh, A. H. P., 'On the asymptotic approximations of the solutions of a system of two non-linearly coupled harmonic oscillators', Journal of Sound and Vibration 49(1), 1976, 93-103.
    • (1976) Journal of Sound and Vibration , vol.49 , Issue.1 , pp. 93-103
    • Van Der Burgh, A.H.P.1
  • 27
    • 0003006808 scopus 로고
    • Why does a mass on a spring sometimes misbehave?
    • Olsson, M. G., 'Why does a mass on a spring sometimes misbehave?', American Journal of Physics 44(12), 1976, 1211-1212.
    • (1976) American Journal of Physics , vol.44 , Issue.12 , pp. 1211-1212
    • Olsson, M.G.1
  • 29
    • 84952278522 scopus 로고
    • Stability of constant amplitude motions in slow-fluctuation approximation
    • Augusteijn, M. and Breitenberger, E., 'Stability of constant amplitude motions in slow-fluctuation approximation', Journal of Mathematical Physics 22(1), 1981, 51-66.
    • (1981) Journal of Mathematical Physics , vol.22 , Issue.1 , pp. 51-66
    • Augusteijn, M.1    Breitenberger, E.2
  • 30
    • 0023647707 scopus 로고
    • Internal resonance of non-linear autonomous vibrating systems with two degrees of freedom
    • Sprysl, H., 'Internal resonance of non-linear autonomous vibrating systems with two degrees of freedom', Journal of Sound and Vibration 112(1), 1987, 63-67.
    • (1987) Journal of Sound and Vibration , vol.112 , Issue.1 , pp. 63-67
    • Sprysl, H.1
  • 31
    • 84983645101 scopus 로고
    • Vibrations of dynamical systems with quadratic nonlinearities
    • Sethna, P. R., 'Vibrations of dynamical systems with quadratic nonlinearities', ASME Journal of Applied Mechanics 32, 1965, 576-582.
    • (1965) ASME Journal of Applied Mechanics , vol.32 , pp. 576-582
    • Sethna, P.R.1
  • 33
    • 0028392575 scopus 로고
    • A global analysis of a harmonically excited spring pendulum system with internal resonance
    • Lee, W. K. and Hsu, C. S., 'A global analysis of a harmonically excited spring pendulum system with internal resonance', Journal of Sound and Vibration 171(3), 1994, 335-359.
    • (1994) Journal of Sound and Vibration , vol.171 , Issue.3 , pp. 335-359
    • Lee, W.K.1    Hsu, C.S.2
  • 36
    • 0008494528 scopus 로고
    • Deterministic Lyapunov exponents from a time series
    • Wolf, A., Swift, J. B., Swinney, H. L., and Vastono, J. A., 'Deterministic Lyapunov exponents from a time series', Physica 16D, 1985, 285-317.
    • (1985) Physica , vol.16 D , pp. 285-317
    • Wolf, A.1    Swift, J.B.2    Swinney, H.L.3    Vastono, J.A.4
  • 37
    • 0009059947 scopus 로고
    • Computation of the largest Lyapunov exponent by the generalized cell mapping
    • Kim, M. C. and Hsu, C. S., 'Computation of the largest Lyapunov exponent by the generalized cell mapping', Journal of Statistical Physics 45, 1986, 49-61.
    • (1986) Journal of Statistical Physics , vol.45 , pp. 49-61
    • Kim, M.C.1    Hsu, C.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.