一类碰撞振动系统的运动和稳定性分析
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摘要
本文通过建立一类碰撞振动系统的运动微分方程,得出系统n-1周期运动存在条件,进而利用碰撞振动系统的poincaré映射的方法,研究了n-1周期运动的稳定性与分岔。最后通过数值模拟分析系统运动的稳定性及分岔。
In this paper,the existence condition of the n-1 periodic motion of the system is obtained by establishing the motion differential equations of vibro-impact system,and then the stability and bifurcation of n-1 periodic motions are studied by the Poincaré maps of vibro-impact system. Finally,the stability and bifurcation of the system were analyzed by numerical simulation.
In this paper,the existence condition of the n-1 periodic motion of the system is obtained by establishing the motion differential equations of vibro-impact system,and then the stability and bifurcation of n-1 periodic motions are studied by the Poincaré maps of vibro-impact system. Finally,the stability and bifurcation of the system were analyzed by numerical simulation.
引文
[1]Luo G W,Zhu X F,Shi Y Q. Dynamics of a two-degree-of freedom periodically-forced system with a rigid stop:Diversity and evolution of periodic-impact motions[J]. Journal of Sound and Vibration,2015(334):338-362.
[2]罗冠炜,谢建华.碰撞振动系统的周期运动和分岔[M].北京:科学出版社,2002:158-169.
[3]Luo G W,Zhu X F,Shi Y Q,et al. Vibration in steam turbine buckets and damping by impact[J]. Engineering,1937,143:305-307.
[4]Arne B,Petri T. Simulation and stability analysis of impacting systems with complete chattering[J]. Nonlinear Dyn,2009(58):85-106.
[5]罗冠炜.两自由度碰撞振动系统的Hopf分岔与混纯研究[D].成都:西南交通大学,1998:66-72.
[6]李群宏,陆启韶.一类双自由度碰振系统运动分析[J].力学学报,2001,33(6):776-786.
[7]Luo G W,Xie J H. Hopf bifurcations and chaos of a two-degree-of-freedom vibro-impact system in two strong resonance cases[J].International Journal of Non-Linear Mechanics,2002(37):19-34.
[2]罗冠炜,谢建华.碰撞振动系统的周期运动和分岔[M].北京:科学出版社,2002:158-169.
[3]Luo G W,Zhu X F,Shi Y Q,et al. Vibration in steam turbine buckets and damping by impact[J]. Engineering,1937,143:305-307.
[4]Arne B,Petri T. Simulation and stability analysis of impacting systems with complete chattering[J]. Nonlinear Dyn,2009(58):85-106.
[5]罗冠炜.两自由度碰撞振动系统的Hopf分岔与混纯研究[D].成都:西南交通大学,1998:66-72.
[6]李群宏,陆启韶.一类双自由度碰振系统运动分析[J].力学学报,2001,33(6):776-786.
[7]Luo G W,Xie J H. Hopf bifurcations and chaos of a two-degree-of-freedom vibro-impact system in two strong resonance cases[J].International Journal of Non-Linear Mechanics,2002(37):19-34.