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Volumn 23, Issue 2, 2000, Pages 105-164

Bifurcations in nonlinear discontinuous systems

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); ORDINARY DIFFERENTIAL EQUATIONS; VIBRATIONS (MECHANICAL);

EID: 0034299647     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008384928636     Document Type: Article
Times cited : (288)

References (53)
  • 2
    • 0004252991 scopus 로고
    • Dover Publications, New York, Reprint. Originally published Pergamon Press, Oxford, 1966 (translated from Russian)
    • Andronov, A. A., Vitt, A. A., and Khaikin, S. E., Theory of Oscillators, Dover Publications, New York, 1987, Reprint. Originally published Pergamon Press, Oxford, 1966 (translated from Russian).
    • (1987) Theory of Oscillators
    • Andronov, A.A.1    Vitt, A.A.2    Khaikin, S.E.3
  • 3
    • 0028460355 scopus 로고
    • A survey of models, analysis tools and compensation methods for the control of machines with friction
    • Armstrong-Hélouvry, B., Dupont, P., and Canudas De Wit, C., 'A survey of models, analysis tools and compensation methods for the control of machines with friction', Automatica 30(7), 1994, 1083-1138.
    • (1994) Automatica , vol.30 , Issue.7 , pp. 1083-1138
    • Armstrong-Hélouvry, B.1    Dupont, P.2    Canudas De Wit, C.3
  • 5
    • 0001551741 scopus 로고    scopus 로고
    • Impact response under the influence of friction
    • Begley, C. J. and Virgin L. N., 'Impact response under the influence of friction', Journal of Sound and Vibration 211(5), 1998, 801-818.
    • (1998) Journal of Sound and Vibration , vol.211 , Issue.5 , pp. 801-818
    • Begley, C.J.1    Virgin, L.N.2
  • 10
    • 0033229544 scopus 로고    scopus 로고
    • Local analysis of C-bifurcations in n-dimensional piecewise-smooth dynamical systems
    • di Bernardo, M., Feigin, M. I., Hogan, S. J., and Homer, M. E., 'Local analysis of C-bifurcations in n-dimensional piecewise-smooth dynamical systems', Chaos, Solitons & Fractals 10(11), 1999, 1881-1908.
    • (1999) Chaos, Solitons & Fractals , vol.10 , Issue.11 , pp. 1881-1908
    • Di Bernardo, M.1    Feigin, M.I.2    Hogans, J.3    Homer, M.E.4
  • 11
    • 0346688041 scopus 로고    scopus 로고
    • On the origin and bifurcations of stick-slip oscillations
    • Dankowicz, H. and Nordmark, A. B., 'On the origin and bifurcations of stick-slip oscillations', Physica D 136(3-4), 2000, 280-302.
    • (2000) Physica D , vol.136 , Issue.3-4 , pp. 280-302
    • Dankowicz, H.1    Nordmark, A.B.2
  • 15
    • 9344246189 scopus 로고    scopus 로고
    • Bifurcations of periodic and chaotic solutions in discontinuous systems
    • Fečkan, M., 'Bifurcations of periodic and chaotic solutions in discontinuous systems', Archivum Mathematicum 34, 1998, 73-82.
    • (1998) Archivum Mathematicum , vol.34 , pp. 73-82
    • Fečkan, M.1
  • 16
    • 21344472534 scopus 로고
    • The increasingly complex structure of the bifurcation tree of a piecewise-smooth system
    • Feigin, M. I., 'The increasingly complex structure of the bifurcation tree of a piecewise-smooth system', Journal of Applied Mathematics and Mechanics 59(6), 1995, 853-863.
    • (1995) Journal of Applied Mathematics and Mechanics , vol.59 , Issue.6 , pp. 853-863
    • Feigin, M.I.1
  • 19
    • 0028516064 scopus 로고
    • Bifurcations in impacting oscillations
    • Foale, S. and Bishop, R., 'Bifurcations in impacting oscillations', Nonlinear Dynamics 6, 1994, 285-299.
    • (1994) Nonlinear Dynamics , vol.6 , pp. 285-299
    • Foale, S.1    Bishop, R.2
  • 20
    • 0031153763 scopus 로고    scopus 로고
    • Event maps in a stick-slip system
    • Galvanetto, U. and Knudsen, C., 'Event maps in a stick-slip system', Nonlinear Dynamics 13(2), 1997, 99-115.
    • (1997) Nonlinear Dynamics , vol.13 , Issue.2 , pp. 99-115
    • Galvanetto, U.1    Knudsen, C.2
  • 26
    • 84962088295 scopus 로고
    • Friction-induced vibration, chatter, squeal and, chaos; Part I: Mechanics of contact and friction; Part II: Dynamics and modeling
    • Ibrahim, R. A., 'Friction-induced vibration, chatter, squeal and, chaos; Part I: Mechanics of contact and friction; Part II: Dynamics and modeling', ASME Applied Mechanics Reviews 47(7), 1994, 209-226, 227-253.
    • (1994) ASME Applied Mechanics Reviews , vol.47 , Issue.7 , pp. 209-226
    • Ibrahim, R.A.1
  • 27
    • 0000223429 scopus 로고    scopus 로고
    • Bifurcations in impact systems
    • Ivanov, A. P., 'Bifurcations in impact systems', Chaos, Solitons & Fractals 7(10), 1996, 1615-1634.
    • (1996) Chaos, Solitons & Fractals , vol.7 , Issue.10 , pp. 1615-1634
    • Ivanov, A.P.1
  • 28
    • 0022027550 scopus 로고
    • Computer simulation of stick-slip friction in mechanical dynamic systems
    • Karnopp, D., 'Computer simulation of stick-slip friction in mechanical dynamic systems', ASME Journal of Dynamic Systems, Measurement and Control 107, 1985, 100-103.
    • (1985) ASME Journal of Dynamic Systems, Measurement and Control , vol.107 , pp. 100-103
    • Karnopp, D.1
  • 29
    • 0039379487 scopus 로고    scopus 로고
    • Qualitative bifurcation analysis of a non-smooth friction oscillator model
    • Kunze, M. and Küpper, T., 'Qualitative bifurcation analysis of a non-smooth friction oscillator model', Zeitschrift für Angewandte Mathematik und Physik 48(1), 1997, 87-101.
    • (1997) Zeitschrift für Angewandte Mathematik und Physik , vol.48 , Issue.1 , pp. 87-101
    • Kunze, M.1    Küpper, T.2
  • 30
  • 32
    • 0001340840 scopus 로고    scopus 로고
    • A mechanism for the onset of chaos in mechanical systems with motion-limiting stops
    • Meijaard, J. P., 'A mechanism for the onset of chaos in mechanical systems with motion-limiting stops', Chaos, Solitons & Fractals 7(10), 1996, 1649-1658.
    • (1996) Chaos, Solitons & Fractals , vol.7 , Issue.10 , pp. 1649-1658
    • Meijaard, J.P.1
  • 33
    • 0345501977 scopus 로고    scopus 로고
    • Efficient numerical integration of the equations of motion of non-smooth mechanical systems
    • Meijaard, J. P., 'Efficient numerical integration of the equations of motion of non-smooth mechanical systems', Zeitschrift für Angewandte Mathematik und Mechanik 77(6), 1997, 419-427.
    • (1997) Zeitschrift für Angewandte Mathematik und Mechanik , vol.77 , Issue.6 , pp. 419-427
    • Meijaard, J.P.1
  • 34
    • 0000442708 scopus 로고
    • Calculation of Lyapunov exponents for dynamic systems with discontinuities
    • Müller, P. C., 'Calculation of Lyapunov exponents for dynamic systems with discontinuities', Chaos, Solitons & Fractals 5(9), 1995, 1671-1681.
    • (1995) Chaos, Solitons & Fractals , vol.5 , Issue.9 , pp. 1671-1681
    • Müller, P.C.1
  • 35
    • 0024752539 scopus 로고
    • Periodic response and stability of oscillators with symmetric trilinear restoring force
    • Natsiavas, S., 'Periodic response and stability of oscillators with symmetric trilinear restoring force', Journal of Sound and Vibration 134(2), 1989, 315-331.
    • (1989) Journal of Sound and Vibration , vol.134 , Issue.2 , pp. 315-331
    • Natsiavas, S.1
  • 36
    • 84998329674 scopus 로고
    • Vibration of harmonically excited oscillators with asymmetric constraints
    • Natsiavas, S. and Gonzalez, H., 'Vibration of harmonically excited oscillators with asymmetric constraints', ASME Journal of Applied Mechanics 59, 1992, 284-290.
    • (1992) ASME Journal of Applied Mechanics , vol.59 , pp. 284-290
    • Natsiavas, S.1    Gonzalez, H.2
  • 37
    • 4244118801 scopus 로고    scopus 로고
    • Universal limit mapping in grazing bifurcations
    • Nordmark, A. B., 'Universal limit mapping in grazing bifurcations', Physical Review E 55(1), 1997, 266-270.
    • (1997) Physical Review E , vol.55 , Issue.1 , pp. 266-270
    • Nordmark, A.B.1
  • 38
    • 44049121950 scopus 로고
    • Border-collision bifurcations including "period two to period three" for piecewise smooth systems
    • Nusse, H. E. and York, J. A., 'Border-collision bifurcations including "period two to period three" for piecewise smooth systems', Physica D 57, 1992, 39-57.
    • (1992) Physica D , vol.57 , pp. 39-57
    • Nusse, H.E.1    York, J.A.2
  • 39
    • 0005150101 scopus 로고    scopus 로고
    • Investigations of low frequency stick-slip motion: Experiments and numerical modelling
    • Oancea, V. G. and Laursen, T. A., 'Investigations of low frequency stick-slip motion: Experiments and numerical modelling', Journal of Sound and Vibration 213(4), 1998, 577-600.
    • (1998) Journal of Sound and Vibration , vol.213 , Issue.4 , pp. 577-600
    • Oancea, V.G.1    Laursen, T.A.2
  • 41
    • 0000792701 scopus 로고    scopus 로고
    • Bifurcations and transition phenomena in an impact oscillator
    • Peterka, F., 'Bifurcations and transition phenomena in an impact oscillator', Chaos, Solitons & Fractals 7(10), 1996, 1635-1647.
    • (1996) Chaos, Solitons & Fractals , vol.7 , Issue.10 , pp. 1635-1647
    • Peterka, F.1
  • 43
    • 51249163979 scopus 로고
    • Dynamical behaviour of a friction oscillator with simultaneous self and external excitation
    • Indian Academy of Sciences, Banglore, India
    • Popp, K., Hinrichs, N., and Oestreich, M., 'Dynamical behaviour of a friction oscillator with simultaneous self and external excitation', in Sādhāna: Academy Proceedings in Engineering Sciences, Indian Academy of Sciences, Banglore, India, Part 2-4, Vol. 20, 1995, pp. 627-654.
    • (1995) Sādhāna: Academy Proceedings in Engineering Sciences , vol.20 , Issue.2-4 PART , pp. 627-654
    • Popp, K.1    Hinrichs, N.2    Oestreich, M.3
  • 46
    • 0001313324 scopus 로고
    • Stability in general control systems
    • Roxin, E., 'Stability in general control systems', Journal of Differential Equations 1, 1965, 115-150.
    • (1965) Journal of Differential Equations , vol.1 , pp. 115-150
    • Roxin, E.1
  • 48
    • 0001658611 scopus 로고
    • Nonlinear vibrations of structures induced by dry friction
    • Stelter, P., 'Nonlinear vibrations of structures induced by dry friction', Nonlinear Dynamics 3, 1992, 329-345.
    • (1992) Nonlinear Dynamics , vol.3 , pp. 329-345
    • Stelter, P.1
  • 51
    • 0032624662 scopus 로고    scopus 로고
    • An approximate analysis of dry-friction-induced stick-slip vibrations by a smoothing procedure
    • Van de Vrande, B. L., Van Campen, D. H., and De Kraker, A., 'An approximate analysis of dry-friction-induced stick-slip vibrations by a smoothing procedure', Nonlinear Dynamics 19(2), 1999, 157-169.
    • (1999) Nonlinear Dynamics , vol.19 , Issue.2 , pp. 157-169
    • Van De Vrande, B.L.1    Van Campen, D.H.2    De Kraker, A.3
  • 52
    • 0000562216 scopus 로고    scopus 로고
    • On modelling discontinuities in dynamic systems
    • Wiercigroch, M., 'On modelling discontinuities in dynamic systems', Machine Vibration 5, 1996, 112-119.
    • (1996) Machine Vibration , vol.5 , pp. 112-119
    • Wiercigroch, M.1
  • 53
    • 0346479918 scopus 로고    scopus 로고
    • Forced self-excited vibration accompanied by dry friction
    • M. Wiercigroch and A. de Kraker (eds.), World Scientific, Singapore, to appear
    • Yoshitake, Y. and Sueoka, A., 'Forced self-excited vibration accompanied by dry friction', in Applied Non-linear Dynamics and Chaos of Mechanical Systems with Discontinuities, M. Wiercigroch and A. de Kraker (eds.), World Scientific, Singapore, 2000 (to appear).
    • (2000) Applied Non-linear Dynamics and Chaos of Mechanical Systems with Discontinuities
    • Yoshitake, Y.1    Sueoka, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.