A global period-1 motion of a periodically excited, piecewise-linear system

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 15, Issue 6, 2005, Pages 1945-1957

  Menon, Santhosh ^a   Luo, Albert C J ^b  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

Author keywords

Mapping; Nonsmooth dynamical system; Periodic motion; Piecewise linear system; Poincar

Indexed keywords

EID: 23944432394     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405013071     Document Type: Article

References (18)

1. Bishop, S. R. [1994] "Analytical determination of bifurcations in an impact oscillators," Philos. Trans. Roy. Soc. London 347, 347-352.
2. Foale, S. [1994] "Analytical determination of bifurcations in an impact oscillators," Philos. Trans. Roy. Soc. London 347, 353-364.
3. Han, R. P. S., Luo, A. C. J. & Deng, W. [1995] "Chaotic motion of a horizontal impact pair," J. Sound Vibr. 181, 231-250.
4. Hartog, J. P. D. & Mikina, S. J. [1932] "Forced vibrations with non-linear spring constants," ASME J. Appl. Mech. 58, 157-164.
5. Hu, H. Y. [1995] "Detection of grazing orbits and incident bifurcations of a forced continuous piecewise linear oscillator," J. Sound Vibr. 187, 485-493.
6. Ivanoy, A. P. [1993] "Stabilization of an impact oscillator near grazing incidence owing to resonance," J. Sound Vibr. 162, 562-565.
7. Kleczka, M., Kreuzer, E. & Schiehlen, W. [1992] "Local and global stability of a piecewise linear oscillator," Philos. Trans.: Phys. Sci. Engin., Nonlin. Dyn. Engin. Syst. 338, 533-546.
8. Luo, A. C. J. & Han, R. P. S. [1996] "Dynamics of a bouncing ball with a periodic vibrating table revisited," Nonlin. Dyn. 10, 1-18.
9. Luo, G. W., Xie, J. H. & Guo, S. H. L. [2000] "Periodic motions and global bifurcations of a two-degree-of-freedom system with plastic vibro-impact," J. Sound Vibr. 240, 837-858.
10. Luo, A. C. J. [2002] "An unsymmetrical motion in a horizontal impact oscillator," ASME J. Vibr. Acoust. 124, 420-426.
11. Natsiavas, S. [1989] "Periodic response and stability of oscillators with symmetric trilinear restoring force," J. Sound Vibr. 134, 315-331.
12. Natsiavas, S. & Verros, G. [1999] "Dynamics of oscillators with strongly nonlinear asymmetric damping," Nonlin. Dyn. 20, 221-246.
13. Nordmark, A. B. [1991] "Non-periodic motion caused by grazing incidence in an impact oscillator," J. Sound Vibr. 145, 279-297.
14. Peterka, F. & Vcacik, J. [1992] "Transition to chaotic motion in mechanical systems with impacts," J. Sound Vibr. 154, 95-115.
15. Shaw, S. W. & Holmes, P. J. [1983] "A periodically forced piecewise linear oscillator," J. Sound Vibr. 90, 121-155.
16. Theodossiades, S. & Natsiavas, S. [2000] "Non-linear dynamics of gear-pair systems with periodic stiffness and backlash," J. Sound Vibr. 229, 287-310.
17. Timoshenko, S., Young, D. H. & Weaver, W. [1974] "Piecewise linear systems," Vibration Problems in Engineering, 4th Edition (D. Van Nostrand, NY), pp. 186-201.
18. Whiston, G. S. [1992] "Singularities in vibro-impact dynamics, " J. Sound Vibr. 152, 427-460.