Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:D3L-A

Session:

Number:891

Derivation Method of the Bifurcation Point for the Periodic Solution in an Impact Oscillator with Periodic Local Cross-Section

Goki Ikeda,  Hiroyuki Asahara,  Kazuyuki Aihara,  Takuji Kousaka,  

pp.891-894

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.891

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Summary:
This paper presents a derivation method of the bifurcation point for the periodic solution in an impact oscillator with periodic local cross-section. First, we explain the impact model and construct the Poincaré map. The construction of the Poincaré map has been subjected by considering presence or absence of the impact. Next, we show the Jacobian matrix and specify the derivative of the Poincaré map to calculate the bifurcation point. Finally, the proposed method is applied for an impact oscillator with periodic local cross-section.

References:

[1] H. Kawakami, “Bifurcation of periodic response in forced dynamic nonlinear circuits: Computation of bifurcation values of the system parameters,” IEEE Trans. Circuits and Syste., Vol. CAS-31, No. 3, pp. 248-260, 1984.

[2] E. Doedel, H. B. Keller and J. P. Kernevez, “Numerical analysis and control of bifurcation problems (I) Bifurcation in finite dimensions,” International Journal of Bifurcation and Chaos, Vol. 1, No. 3, pp. 493-520, 1991.

[3] http://bunki.sat.iis.u-tokyo.ac.jp/BUNKI/

[4] K. Karagiannis and F. Pfeiffer, “Theoretical and experimental investigations of gear-rattling,” NONLINEAR DYNAMICS, Vol. 2, No. 5, pp. 367-387, 1991.

[5] F. Pfeiffer and A. Kunert, “Rattling models from deterministic to stochastic processes,” NONLINEAR DYNAMICS, Vol. 1, No. 1, pp. 63-74, 1990.

[6] G. X. Li and M. P. Païdoussis “Impact phenomena of rotor-casing dynamical systems,” NONLINEAR DYNAMICS, Vol. 5, No. 1, pp. 53-70, 1994.

[7] Barbara Blazejczyk-Okolewska, “Analysis of an impact damper of vibrations,” Chaos, Solitons and Fractals, Vol. 12, No. 11, pp. 1983-1988, 2000.

[8] Y. Yoshitake, A. Sueoka, T. Miyuki, T. Hamano, S. Kitayama, S. Tamura, “Development of Shooting Method for Impact Systems,” JSME International Series C, Vol. 47, No. 3, pp. 834-844, 2004.

[9] G. Ikeda, K. Aihara, and T. Kousaka, “Calculation Method of Bifurcation Point for an Impact Oscillator with Periodic Function,” The 5th International Conference on Chaotic Modeling and Simulation, CHAOS 2012, Athens, Greece, 2012. (In press)

[10] S. Kawamura, K. Kitajo, S. Horita and M. Yoshizawa, “Fundamental Study on Impact Oscillations of Rigid Trolley-Pantograph System,” The Japan Society of Mechanical Engineers, Series C, Vol. 73, No. 728, pp. 974-981, 2007(In Japanese).