Study on a new nonlinear parametric excitation equation: Stability and bifurcation
作者： Chen Si-yu , Tang Jin-yuan , None
DOI: 10.1016/J.JSV.2008.04.055
关键词:
摘要: Anstract The parameter stability and global bifurcations of a strong nonlinear system with parametric excitation external excitations are investigated in detail. Using the method Multiple scales, is transformed to averaged equation. solution case principal resonance developed. Based on equation, continuation algorithm utilized analyze detailed bifurcation scenario as f0 varied. results indicate that there exist two limit points neutral saddle points. Finally, series branching were obtained by changing parameters ρ.
harvard.edu
elsevier.com
sci-hub.se 参考文章(17)
Andrei Yu Kolesov, Nikolai Kh Rozov, Parametric excitation of high-mode oscillations for a non-linear telegraph equation Sbornik Mathematics. ,vol. 191, pp. 1147- 1169 ,(2000) , 10.1070/SM2000V191N08ABEH000498
Leslie Ng, Richard Rand, Bifurcations in a Mathieu equation with cubic nonlinearities Chaos Solitons & Fractals. ,vol. 14, pp. 173- 181 ,(2002) , 10.1016/S0960-0779(01)00226-0
A. M. Elnaggar, A. A. Alhanadwah, Parametric excitation of subharmonic oscillations International Journal of Theoretical Physics. ,vol. 36, pp. 1921- 1940 ,(1997) , 10.1007/BF02435853
E. Esmailzadeh, G. Nakhaie-jazar, Periodic solution of a Mathieu-Duffing type equation International Journal of Non-linear Mechanics. ,vol. 32, pp. 905- 912 ,(1997) , 10.1016/S0020-7462(96)00119-9
A.F. El-Bassiouny, On methods for continuous systems with quadratic, cubic and quantic nonlinearities Chaos, Solitons & Fractals. ,vol. 39, pp. 1308- 1316 ,(2009) , 10.1016/J.CHAOS.2007.06.021
Anastasia Sofroniou, Steven R. Bishop, Breaking the symmetry of the parametrically excited pendulum Chaos, Solitons & Fractals. ,vol. 28, pp. 673- 681 ,(2006) , 10.1016/J.CHAOS.2005.07.014
Qinglong Ma, A. Kahraman, Subharmonic resonances of a mechanical oscillator with periodically time-varying, piecewise-nonlinear stiffness Journal of Sound and Vibration. ,vol. 294, pp. 624- 636 ,(2006) , 10.1016/J.JSV.2005.11.026
S. Natsiavas, S. Theodossiades, I. Goudas, Dynamic analysis of piecewise linear oscillators with time periodic coefficients International Journal of Non-linear Mechanics. ,vol. 35, pp. 53- 68 ,(2000) , 10.1016/S0020-7462(98)00087-0
R.R.A. Coles, C.G. Rice, Earplugs and impaired hearing Journal of Sound and Vibration. ,vol. 3, pp. 521- 523 ,(1966) , 10.1016/0022-460X(66)90113-1
K. Szabelski, J. Warminski, SELF-EXCITED SYSTEM VIBRATIONS WITH PARAMETRIC AND EXTERNAL EXCITATIONS Journal of Sound and Vibration. ,vol. 187, pp. 595- 607 ,(1995) , 10.1006/JSVI.1995.0547