含预压约束的两自由度受迫振动系统的动力学特性
|
摘要
振动现象广泛存在于各类机械系统中,使得系统表现出复杂的动力学行为.对含预压约束的振动系统动力学特性的分析为工业实际中含预压约束机械系统的优化设计提供了理论依据.因此建立了一类含预压约束的两自由度受迫振动系统的力学模型.通过数值仿真,对系统的周期碰撞特性进行了研究,讨论了亚谐波运动1/(n+1)与1/n之间的转迁规律,分析了预压量的变化对系统产生的影响.结果表明:高频时,随外激励频率的减小系统的亚谐波运动1/(n+1)首先通过倍化分岔、擦切分岔通向混沌或长周期运动,再由混沌或长周期运动通过逆倍化分岔演变为1/n运动;低频时,增大预压量d,系统中的非完全颤振会通过Sliding分岔转迁为完全颤振运动,减小预压量d,系统中非完全颤振情况消失演变为基本周期运动.由此可知,低频时预压约束的存在对受迫振动系统的动力学特性有显著的影响.
Vibration phenomena widely exist in various types of mechanical systems and cause the complex dynamic behaviors of the system.The analysis of dynamic characteristics in vibration systems provides a theoretical basis for the optimization design of mechanical system with preloading constraint in industrial practice.Therefore,a dynamic model of a two-degree-of-freedom forced vibration system with preload constraints is set up.Through the numerical simulation,the periodic collision characteristics of the system are studied,the transition law between the subharmonic motion 1/(n+1) and 1/n is discussed,and the effect of preload variation on the system is analyzed.The results show that the subharmonic motion 1/(n+1) of the system first leads to chaotic or long-period motion through doubling bifurcation and grazing bifurcation,then from chaotic or long-period motion to 1/n motion through inverse doubling bifurcation at high frequencies.At low frequencies,with the increase of preload d,the incomplete chatter in the system will change to complete chatter motion through sliding bifurcation.By reducing the preload d,the incomplete chatter in the system disappears and becomes a basic periodic motion.It can be concluded that the existence of preloading constraint has a great influence on the dynamic characteristics of forced vibration system at low frequencies.
Vibration phenomena widely exist in various types of mechanical systems and cause the complex dynamic behaviors of the system.The analysis of dynamic characteristics in vibration systems provides a theoretical basis for the optimization design of mechanical system with preloading constraint in industrial practice.Therefore,a dynamic model of a two-degree-of-freedom forced vibration system with preload constraints is set up.Through the numerical simulation,the periodic collision characteristics of the system are studied,the transition law between the subharmonic motion 1/(n+1) and 1/n is discussed,and the effect of preload variation on the system is analyzed.The results show that the subharmonic motion 1/(n+1) of the system first leads to chaotic or long-period motion through doubling bifurcation and grazing bifurcation,then from chaotic or long-period motion to 1/n motion through inverse doubling bifurcation at high frequencies.At low frequencies,with the increase of preload d,the incomplete chatter in the system will change to complete chatter motion through sliding bifurcation.By reducing the preload d,the incomplete chatter in the system disappears and becomes a basic periodic motion.It can be concluded that the existence of preloading constraint has a great influence on the dynamic characteristics of forced vibration system at low frequencies.
引文
[1] 罗冠炜,张艳龙,谢建华.含对称刚性约束振动系统的周期运动和分岔[J].工程力学,2007,24(7):44-52.
[2] LUO G W,Lü X H.Controlling bifurcation and chaos of a plastic impact oscillator[J].Nonlinear Analysis:Real World Applications,2008,10(4):2047-2061.
[3] 吕小红,罗冠炜.碰撞-渐进振动系统的周期振动与分岔[J].振动与冲击,2018,37(6):162-167.
[4] 朱喜锋,罗冠炜.两自由度含间隙弹性碰撞系统的颤碰运动分析[J].振动与冲击,2015,34(15):195-200.
[5] 吕小红.冲击振动系统的粘滞振动及分岔特性研究[D].兰州:兰州交通大学,2016.
[6] 朱喜锋.含间隙机械系统的动力学特性及参数匹配规律研究[D].兰州:兰州交通大学,2016.
[7] 侍玉青,赵琳燕,姜春霞.含摩擦和间隙振动系统的低频动力学特征[J].兰州交通大学学报,2017,36(6):8-12.
[8] 赵琳燕,侍玉青,姜春霞.一类存在间隙和摩擦的分段光滑振动系统的动力学特性[J].兰州交通大学学报,2014,33(3):41-45.
[9] 姜春霞,边红丽,赵琳燕,等.一类摩擦碰撞振动系统的周期振动特性研究[J].兰州交通大学学报,2013,32(6):181-185.
[10] KUNDU S,BANERJEE S,ING J,et al.Singularities in soft-impacting systems[J].Physica D Nonlinear Phenomena,2012,241(5):553-565.
[11] MA Y,AGARWAL M,BANERJEE S.Border collision bifurcations in a soft impact system[J].Physics Letters A,2006,354(4):281-287.
[12] 张惠,丁旺才,褚衍东,等.非光滑动力系统局部奇异性及擦边条件分析[J].兰州交通大学学报,2015,34(4):150-156.
[2] LUO G W,Lü X H.Controlling bifurcation and chaos of a plastic impact oscillator[J].Nonlinear Analysis:Real World Applications,2008,10(4):2047-2061.
[3] 吕小红,罗冠炜.碰撞-渐进振动系统的周期振动与分岔[J].振动与冲击,2018,37(6):162-167.
[4] 朱喜锋,罗冠炜.两自由度含间隙弹性碰撞系统的颤碰运动分析[J].振动与冲击,2015,34(15):195-200.
[5] 吕小红.冲击振动系统的粘滞振动及分岔特性研究[D].兰州:兰州交通大学,2016.
[6] 朱喜锋.含间隙机械系统的动力学特性及参数匹配规律研究[D].兰州:兰州交通大学,2016.
[7] 侍玉青,赵琳燕,姜春霞.含摩擦和间隙振动系统的低频动力学特征[J].兰州交通大学学报,2017,36(6):8-12.
[8] 赵琳燕,侍玉青,姜春霞.一类存在间隙和摩擦的分段光滑振动系统的动力学特性[J].兰州交通大学学报,2014,33(3):41-45.
[9] 姜春霞,边红丽,赵琳燕,等.一类摩擦碰撞振动系统的周期振动特性研究[J].兰州交通大学学报,2013,32(6):181-185.
[10] KUNDU S,BANERJEE S,ING J,et al.Singularities in soft-impacting systems[J].Physica D Nonlinear Phenomena,2012,241(5):553-565.
[11] MA Y,AGARWAL M,BANERJEE S.Border collision bifurcations in a soft impact system[J].Physics Letters A,2006,354(4):281-287.
[12] 张惠,丁旺才,褚衍东,等.非光滑动力系统局部奇异性及擦边条件分析[J].兰州交通大学学报,2015,34(4):150-156.