Synchronisation and Chaos in a Parametrically and Self-Excited System with Two Degrees of Freedom

被引：17
作者：
Jerzy Warmiński
Grzegorz Litak
Kazimierz Szabelski
机构：
[1] Technical University of Lublin,Department of Applied Mechanics
来源：
Nonlinear Dynamics | 2000年 / 22卷 / 2期
关键词：
chaos; vibrations; self-excited system; parametric excitation;
D O I：
10.1023/A:1008325924199
中图分类号：
学科分类号：
摘要：
Vibration analysis of a non-linear parametrically andself-excited system of two degrees of freedom was carried out. The modelcontains two van der Pol oscillators coupled by a linear spring with a aperiodically changing stiffness of the Mathieu type. By means of amultiple-scales method, the existence and stability of periodicsolutions close to the main parametric resonances have beeninvestigated. Bifurcations of the system and regions of chaoticsolutions have been found. The possibility of the appearance ofhyperchaos has also been discussed and an example of such solution hasbeen shown.
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页码：125 / 143
页数：18
相关论文
共 25 条
[1]  
Yano S. '.(1989)Considerations on self-and parametrically excited vibrational systems Ingenieur-Archiv 59 285-295
[2]  
Szabelski K.(1997)The non-linear vibrations of parametrically self-excited system with two degrees of freedom under external excitation Nonlinear Dynamics 14 23-36
[3]  
Warmiński J. '.(1999)Vibration analysis of a self-excited system with parametric forcing and nonlinear stiffness International Journal of Bifurcation and Chaos 9 493-504
[4]  
Litak G.(1995)The parametric self excited non-linear system vibrations analysis with the inertial excitation International Journal of Non-Linear Mechanics 30 179-189
[5]  
Szabelski K.(1995)The self excited system vibrations with the parametric and external excitations Journal of Sound and Vibration 908 595-607
[6]  
Spuz-Szpos G.(1999)Vibration of externally forced Froude pendulum International Journal of Bifurcation and Chaos 9 561-570
[7]  
Warmiński J. '.(1996)Locally-intermingled basins of attraction in coupled Chua's circuits International Journal of Bifurcation and Chaos 6 357-366
[8]  
Szabelski K.(1993)Transition to chaos in chaotically forced coupled oscillators Physical Review E47 R2975-R2978
[9]  
Warmiński J. '.(1994)Hyperchaotic attractors of undirectionally-coupled Chua's circuits International Journal of Bifurcation and Chaos 4 477-482
[10]  
Szabelski K.(1991)Transition to hyperchaos in coupled generalized Van der Pol's equations Physics Letters A152 33-37
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