메뉴 건너뛰기




Volumn 148, Issue 3-4, 2001, Pages 183-200

Bifurcations and chaos in a system with impacts

Author keywords

Bouncing; Chaos; Hopf bifurcation; Map; Strong resonance; Subharmonic bifurcation; Vibro impact

Indexed keywords


EID: 0347572319     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(00)00170-6     Document Type: Article
Times cited : (72)

References (26)
  • 1
    • 0020185856 scopus 로고
    • The dynamics of repeated impacts with a sinusoidally vibrating table
    • P.J. Holmes, The dynamics of repeated impacts with a sinusoidally vibrating table, J. Sound Vibration 84 (2) (1982) 173-189.
    • (1982) J. Sound Vibration , vol.84 , Issue.2 , pp. 173-189
    • Holmes, P.J.1
  • 2
    • 0021097823 scopus 로고
    • A periodically forced piece wise linear oscilinear
    • S.W. Shaw, P.J. Holmes, A periodically forced piece wise linear oscilinear, J. Sound Vibration 90 (1983) 129-155.
    • (1983) J. Sound Vibration , vol.90 , pp. 129-155
    • Shaw, S.W.1    Holmes, P.J.2
  • 3
    • 18444414036 scopus 로고
    • Chaos after period-doubling bifurcations in the resonance of an impact oscillator
    • J.M.T. Thompson, Chaos after period-doubling bifurcations in the resonance of an impact oscillator, Phys. Lett. 91A (1983) 5-8.
    • (1983) Phys. Lett. , vol.91 A , pp. 5-8
    • Thompson, J.M.T.1
  • 4
    • 0009370405 scopus 로고
    • Periodically forced linear oscillator with impacts: Chaos and long-period motions
    • S.W. Shaw, P.J. Holmes, Periodically forced linear oscillator with impacts: chaos and long-period motions, Phys. Rev. Lett. 51 (8) (1983) 623-626.
    • (1983) Phys. Rev. Lett. , vol.51 , Issue.8 , pp. 623-626
    • Shaw, S.W.1    Holmes, P.J.2
  • 5
    • 0023648534 scopus 로고
    • Global dynamics of vibro-impact oscillation
    • G.S. Whiston, Global dynamics of vibro-impact oscillation, J. Sound Vibration 118 (3) (1987) 395-429.
    • (1987) J. Sound Vibration , vol.118 , Issue.3 , pp. 395-429
    • Whiston, G.S.1
  • 6
    • 0027912129 scopus 로고
    • Periodic and chaotic behaviour of a threshold-limited two-degree-of-freedom system
    • J.O. Aidanpaa, B.R. Gupta, Periodic and chaotic behaviour of a threshold-limited two-degree-of-freedom system, J. Sound Vibration 165 (2) (1992) 305-327.
    • (1992) J. Sound Vibration , vol.165 , Issue.2 , pp. 305-327
    • Aidanpaa, J.O.1    Gupta, B.R.2
  • 7
    • 0026187991 scopus 로고
    • Two-dimensional vibratory impact with chaos
    • J.E. Kozol, R.M. Brach, Two-dimensional vibratory impact with chaos, J. Sound Vibration 148 (2) (1991) 319-327.
    • (1991) J. Sound Vibration , vol.148 , Issue.2 , pp. 319-327
    • Kozol, J.E.1    Brach, R.M.2
  • 8
    • 0026419524 scopus 로고
    • Non-periodic motion caused by grazing incidence in an impact oscillator
    • A.B. Nordmark, Non-periodic motion caused by grazing incidence in an impact oscillator, J. Sound Vibration 145 (2) (1991) 279-297.
    • (1991) J. Sound Vibration , vol.145 , Issue.2 , pp. 279-297
    • Nordmark, A.B.1
  • 9
    • 0027114865 scopus 로고
    • Singularities in vibro-impact dynamics
    • G.S. Whiston, Singularities in vibro-impact dynamics, J. Sound Vibration 152 (3) (1992) 427-460.
    • (1992) J. Sound Vibration , vol.152 , Issue.3 , pp. 427-460
    • Whiston, G.S.1
  • 10
    • 0027114979 scopus 로고
    • Transition to chaotic motion in mechanical systems with impacts
    • F. Peterka, J. Vcacik, Transition to chaotic motion in mechanical systems with impacts, J. Sound Vibration 154 (1) (1992) 95-115.
    • (1992) J. Sound Vibration , vol.154 , Issue.1 , pp. 95-115
    • Peterka, F.1    Vcacik, J.2
  • 11
    • 0002050467 scopus 로고
    • Bifurcations in impact oscillators: Theory and experiments
    • J.M.T. Thompson (Ed.), Wiley, Chichester, UK
    • S. Foale, S.R. Bishop, Bifurcations in impact oscillators: theory and experiments, in: J.M.T. Thompson (Ed.), Nonlinearity and Chaos in Engineering Dynamics, Wiley, Chichester, UK, 1994, pp. 91-102.
    • (1994) Nonlinearity and Chaos in Engineering Dynamics , pp. 91-102
    • Foale, S.1    Bishop, S.R.2
  • 12
    • 0027576057 scopus 로고
    • Stabilization of an impact oscillator near grazing incidence owing to resonance
    • A.P. Ivanov, Stabilization of an impact oscillator near grazing incidence owing to resonance, J. Sound Vibration 162 (3) (1993) 562-565.
    • (1993) J. Sound Vibration , vol.162 , Issue.3 , pp. 562-565
    • Ivanov, A.P.1
  • 13
    • 0000223429 scopus 로고    scopus 로고
    • Bifurcation in impact systems
    • A.P. Ivanov, Bifurcation in impact systems, Solitons and Fractals 7 (10) (1996) 1615-1634.
    • (1996) Solitons and Fractals , vol.7 , Issue.10 , pp. 1615-1634
    • Ivanov, A.P.1
  • 14
    • 0000792701 scopus 로고    scopus 로고
    • Bifurcation and transition phenomena in an impact oscillator
    • F. Peterka, Bifurcation and transition phenomena in an impact oscillator, Solitons and Fractals 7 (10) (1996) 1635-1647.
    • (1996) Solitons and Fractals , vol.7 , Issue.10 , pp. 1635-1647
    • Peterka, F.1
  • 15
    • 0029771253 scopus 로고    scopus 로고
    • Codimension two bifurcations and Hopf bifurcations of an impacting vibrating system
    • J.H. Xie, Codimension two bifurcations and Hopf bifurcations of an impacting vibrating system, Appl. Math. Mech. 17 (1996) 65-75.
    • (1996) Appl. Math. Mech. , vol.17 , pp. 65-75
    • Xie, J.H.1
  • 16
    • 0027642864 scopus 로고
    • Dynamics of multiple-degree-of-freedom oscillations with colliding components
    • S. Natsiavas, Dynamics of multiple-degree-of-freedom oscillations with colliding components, J. Sound Vibration 165 (3) (1993) 439-453.
    • (1993) J. Sound Vibration , vol.165 , Issue.3 , pp. 439-453
    • Natsiavas, S.1
  • 17
    • 0030126929 scopus 로고    scopus 로고
    • Bifurcations and chaos in autonomous self-excited oscillators with impact damping
    • S. Chatterjee, A.K. Mallik, Bifurcations and chaos in autonomous self-excited oscillators with impact damping, J. Sound Vibration 191 (4) (1996) 539-562.
    • (1996) J. Sound Vibration , vol.191 , Issue.4 , pp. 539-562
    • Chatterjee, S.1    Mallik, A.K.2
  • 18
    • 33747072063 scopus 로고
    • The effect of frequency and clearance variations on single-degree-of-freedom impact oscillators
    • C. Budd, F. Dux, A. Cliffe, The effect of frequency and clearance variations on single-degree-of-freedom impact oscillators, J. Sound Vibration 184 (3) (1995) 475-502.
    • (1995) J. Sound Vibration , vol.184 , Issue.3 , pp. 475-502
    • Budd, C.1    Dux, F.2    Cliffe, A.3
  • 19
    • 0000760062 scopus 로고    scopus 로고
    • Hopf bifurcation of a two-degree-of-freedom vibro-impact system
    • G.W. Luo, J.H. Xie, Hopf bifurcation of a two-degree-of-freedom vibro-impact system, J. Sound Vibration 213 (3) (1998) 391-408.
    • (1998) J. Sound Vibration , vol.213 , Issue.3 , pp. 391-408
    • Luo, G.W.1    Xie, J.H.2
  • 21
    • 0003289284 scopus 로고
    • Applications of Centre Manifold Theory
    • Springer, Berlin
    • J. Car, Applications of Centre Manifold Theory, Applied Mathematical Sciences, Vol. 35, Springer, Berlin, 1981, pp. 33-36.
    • (1981) Applied Mathematical Sciences , vol.35 , pp. 33-36
    • Car, J.1
  • 22
    • 0000480907 scopus 로고
    • Bifurcation of Maps and Applications
    • North-Holland, Amsterdam
    • G. Iooss, Bifurcation of Maps and Applications, Mathematics Studies, Vol. 36, North-Holland, Amsterdam, 1979, pp. 201-222.
    • (1979) Mathematics Studies , vol.36 , pp. 201-222
    • Iooss, G.1
  • 23
    • 0002945542 scopus 로고
    • Loss of stability of oscillations close to resonance and versal deformations of equivariant vector fields
    • V.I. Arnold, Loss of stability of oscillations close to resonance and versal deformations of equivariant vector fields, Funk. Anal. Ego. Prilog. 11 (1977) 1-10.
    • (1977) Funk. Anal. Ego. Prilog. , vol.11 , pp. 1-10
    • Arnold, V.I.1
  • 24
    • 0005154434 scopus 로고
    • Bifurcation into invariant tori at points of resonance
    • Y.-H. Wan, Bifurcation into invariant tori at points of resonance, Arch. Rational Mech. Anal. 68 (1978) 343-357.
    • (1978) Arch. Rational Mech. Anal. , vol.68 , pp. 343-357
    • Wan, Y.-H.1
  • 25
    • 0000053184 scopus 로고
    • Oscillation and doubling of torus
    • K. Kaneko, Oscillation and doubling of torus, Prog. Theoret. Phys. 72 (2) (1984) 202-215.
    • (1984) Prog. Theoret. Phys. , vol.72 , Issue.2 , pp. 202-215
    • Kaneko, K.1
  • 26
    • 0002157922 scopus 로고
    • Cascade of period doublings of tori
    • A. Arneodo, P.H. Coullet, Cascade of period doublings of tori, Phys. Lett. 94A (1) (1983) 1-6.
    • (1983) Phys. Lett. , vol.94 A , Issue.1 , pp. 1-6
    • Arneodo, A.1    Coullet, P.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.