Bifurcation and chaos of a harmonically excited oscillator with both stiffness and viscous damping piecewise linearities by incremental harmonic balance method

Journal of Sound and Vibration

Volumn 264, Issue 4, 2003, Pages 873-882

  Xu, L ^a   Lu, M W ^a   Cao, Q ^b  

^a TSINGHUA UNIVERSITY   (China)

^b SHANDONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; DAMPING; HARMONIC ANALYSIS; INTEGRATION; PIECEWISE LINEAR TECHNIQUES; STIFFNESS;

LINKAGE JOINTS;

OSCILLATORS (MECHANICAL);

EID: 0037698267     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-460X(02)01194-X     Document Type: Article

References (20)

1. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, New York, 1990.
2. K. Murali, M. Lakshmanan, L.O. Chua, The simplest dissipative nonautomous chaotic circuit, IEEE Transactions on Circuits and Systems 41 (1994) 462-463.
3. Y.S. Choi, S.T. Noah, Forced periodic vibration of unsymmetric piecewise-linear systems, Journal of Sound and Vibration 121 (1988) 117-126.
4. S. Maezawa, H. Kumano, Y. Minakuchi, Forced vibrations in an unsymmetric piecewise-linear system excited by general periodic force functions, Bulletin of the JSME 23 (1980) 68-75.
5. J.M. Thompson, Complex dynamics of compliant off shore structures, Proceedings of the Royal Society of London 387 (1983) 407-427.
6. J.M. Thompson, A.R. Bokain, R. Ghaffari, Subharmonic resonances and chaotic motions of the bilinear oscillator, IMA Journal of Applied Mathematics 31 (1983) 207-234.
7. J.L. Hudson, H.C. Killory, Chaos in a four-variable piecewise-linear system of differential equations, IEEE Transactions on Circuits and Systems 35 (1998) 902-908.
8. T. Matsumoto, L.O. Chua, K. Kobayashi, Hyperchaos: laboratory experiment and numerical confirmation, IEEE Transactions on Circuits and Systems 33 (1986) 1143-1147.
9. J.J. Stijer, Nonlinear Vibrations in Mechanical and Electrical Systems, Wiley, New York, 1992.
10. S.L. Lau, Y.K. Cheung, Amplitude incremental variational principle for nonlinear vibration of elastic system, American Society of Mechanical Engineers, Journal of Applied Mechanics 48 (1981) 959-964.
11. S.L. Lau, S.W. Yuen, Solution diagram of nonlinear dynamic systems by the IHB method, Journal of Sound and Vibration 167(1993) 303-316.
12. A. Raghothama, S. Narayanan, Bifurcation and chaos in escape equation model by incremental harmonic balancing, Chaos Solitons & Fractals 11 (2000) 1349-1363.
13. A. Raghothama, S. Narayanan, Bifurcation and chaos of an articulated loading platform with piecewise non-linear stiffness using the incremental harmonic balance method, Ocean Engineering 27 (2000) 1087-1107.
14. C. Pierre, A.A. Ferri, E.H. Dowell, Multi-harmonic analysis of dry friction damped systems using an incremental harmonic balance method, Journal of Applied Mechanics 52 (1985) 958-964.
15. C.W. Wong, W.S. Zhang, S.L. Lau, Periodic forced vibration of unsymmetrical piecewise-linear systems by incremental harmonic balance method, Journal of Sound and Vibration 149 (1991) 91-105.
16. S.L. Lau, W.S. Zhang, Nonlinear vibrations of piecewise-linear systems by incremental harmonic balance method, Journal of Applied Mechanics 59 (1992) 153-160.
17. Q. Cao, L. Xu, K. Djidjeli, Analysis of period-doubling and chaos of a non-symmetric oscillator with piecewise-linearity, Chaos Solitons & Fractals 12 (2001) 1917-1927.
18. T.Y. Li, J.A. Yorke, Period three implies chaos, American Math Monthly 82 (1975) 985-990.
19. B.H. Tongue, K. Gu, Interpolated cell mapping of dynamical Systems, Journal of Applied Mechanics 55 (1988) 461-466.
20. J. Guckenheimer, P. Holmes, Nonlinear Oscillation Dynamical Systems and Bifurcation of Vector Fields, Springer, New York, 1983.