The mapping dynamics of periodic motions for a three-piecewise linear system under a periodic excitation

Journal of Sound and Vibration

Volumn 283, Issue 3-5, 2005, Pages 723-748

  Luo, Albert C J ^a  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; DYNAMIC RESPONSE; PIECEWISE LINEAR TECHNIQUES; POWER CONTROL; VIBRATION CONTROL;

MAPPING DYNAMICS; MAPPING STRUCTURES; PERIODIC MOTIONS; TRI-LINEAR SPRINGS;

MOTION ESTIMATION;

EID: 15944409254     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsv.2004.05.023     Document Type: Article

References (20)

1. H. Poincaré, Les Methods Nouvelles de la Mecanique Celeste, vol. 1, Gauthier-Villars, Paris, 1892.
2. C.D. Birkhoff On the periodic motions of dynamical systems Acta Mathematica 50 1927 359 379
3. E.A. Corddington, and N. Levinson Theory of Ordinary Differential Equations 1955 McGraw-Hill New York
4. M. Henon, and C. Heiles The applicability of the third integral motion some numerical experiments Astronomical Journal 69 1964 73 79
5. Y. Ueda Steady motion exhibited by Duffing's equation a picture book of regular and chaotic motion P.J. Holmes New Approaches to Nonlinear Problems in Dynamics 1980 SIAM Philadelphia 311 322
6. S.W. Shaw, and P.J. Holmes A periodically forced piecewise linear oscillator Journal of Sound and Vibration 90 1 1983 121 155
7. A.B. Nordmark Non-periodic motion caused by grazing incidence in an impact oscillator Journal of Sound and Vibration 145 1991 279 297
8. M. Kleczka, E. Kreuzer, and W. Schiehlen Local and global stability of a piecewise linear oscillator Philosophical Transactions of the Royal Society of London Physical Sciences and Engineering, Nonlinear Dynamics of Engineering Systems 338 1992 533 546
9. S. Foale Analytical determination of bifurcations in an impact oscillators Philosophical Transactions of the Royal Society of London 347 1994 353 364
10. A.C.J. Luo, Analytical Modeling of Bifurcations, Chaos and Multifactals in Nonlinear Dynamics, Ph.D. Dissertation, University of Manitoba, Manitoba, Canada, 1995.
11. R.P.S. Han, A.C.J. Luo, and W. Deng Chaotic motion of a horizontal impact pair Journal of Sound and Vibration 181 1995 231 250
12. A.C.J. Luo, and R.P.S. Han Dynamics of a bouncing ball with a periodic vibrating table revisited Nonlinear Dynamics 10 1996 1 18
13. A.C.J. Luo An unsymmetrical motion in a horizontal impact oscillator Journal of Vibrations and Acoustics 124 2002 420 426
14. G.X. Li, R.H. Rand, and F.C. Moon Bifurcation and chaos in a forced zero-stiffness impact oscillator International Journal of Nonlinear Mechanics 25 4 1990 414 432
15. S. Menon, A.C.J. Luo, An analytical prediction of the global period-1 motion in a periodically forced, piecewise linear system, International Journal of Bifurcation and Chaos, in press.
16. J.P.D. Hartog, and S.J. Mikina Forced vibrations with non-linear spring constants Journal of Applied Mechanics 58 1932 157 164
17. S. Timoshenko Vibration Problems in Engineering 1937 Van Nostrand New York
18. S. Natsiavas Periodic response and stability of oscillators with symmetric trilinear restoring force Journal of Sound and Vibration 134 2 1989 315 331
19. S. Natsiavas, and G. Verros Dynamics of oscillators with strongly nonlinear asymmetric damping Nonlinear Dynamics 20 1999 221 246
20. S. Theodossiades, and S. Natsiavas Non-linear dynamics of gear-pair systems with periodic stiffness and backlash Journal of Sound and Vibration 229 2 2000 287 310