| Original Articles |
|
|
|
|
Heteroclinic Bifurcation of Strongly Nonlinear Oscillator |
| ZHANG Qi-Chang;WANG Wei;LI Wei-Yi |
| Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300072State key Laboratory of Engines, Tianjin University, Tianjin 300072 |
|
| Cite this article: |
|
ZHANG Qi-Chang, WANG Wei, LI Wei-Yi 2008 Chin. Phys. Lett. 25 1905-1907 |
|
|
|
Abstract Analytical prediction of heteroclinic bifurcation of the strongly nonlinear oscillator is presented by using the extended normal form method. We consider the approximate periodic solution of the system subject to the quintic nonlinearity by introducing the undetermined fundamental frequency. For the occurrence of heteroclinicity, the bifurcation criterion is accomplished. It depends on the contact of the limit cycle with the saddle equilibrium. As is illustrated, the explicit application shows that the new results coincide very well with the results of numerical simulation when disturbing parameter is of
arbitrary magnitude.
|
| Keywords:
82.40.Bj
47.20.Ky
02.30.Hq
|
|
|
Received: 20 February 2008
Published: 29 April 2008
|
|
| PACS: |
82.40.Bj
|
(Oscillations, chaos, and bifurcations)
|
| |
47.20.Ky
|
(Nonlinearity, bifurcation, and symmetry breaking)
|
| |
02.30.Hq
|
(Ordinary differential equations)
|
|
|
|
|
|
[1]Melnikov V K 1963 Trans. Moscow Math. Soc. 12 1
[2] Guckenheimer J, Holmes P J 1983 NonlinearOscillations, Dynamical Systems and Bifurcations of Vector Fields(New York: Springer) p 369
[3] Belhaq M and Fahsi A 1996 Mech. Res. Commun. 23381
[4] Belhaq M 1998 Mech. Res. Commun. 25 49
[5] Belhaq M, Lakrad F and Fahsi A 1999 Nonlinear Dynam. 18 303
[6] Xu Z, Chen S H 1997 Acta Scientiarum NaturaliumUniversitatis Sunyatsen 36 6 (in Chinese)
[7] Belhaq M, Fiedler B and Lakrad F 2000 NonlinearDynam. 23 67
[8] Zhang Y M, Lu Q S 2003 Nonlinear Sci. Numer.Simulat. 8 1
[9] Leung A Y T, Zhang Q C 1998 J. Sound Vib. 213907
[10] Hao S Y, Wang W, Zhang Q C 2007 J. Vibrat.Engin. 422 20 (in Chinese)
[11] Nayfeh A H 1983 Method of Normal Forms (New York: Wiley) p 14 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
