含摩擦和间隙振动系统的低频动力学特征
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摘要
建立含摩擦和间隙的两自由度振动系统动力学模型,采用四阶Runge-Kutta数值积分法,研究受简谐激励力作用的系统动力学特征.分析了基准参数下系统呈现的低频粘滞和非粘滞周期振动及分岔特点,讨论了间隙对系统周期冲击振动、分岔及滑移-粘滞状态的影响.研究结果表明,随着间隙增大,系统的动力学行为变得更为简单,质量块与皮带轮粘滞的频率带减小.
A two-degrees-freedom vibration system with two clearances and dry friction is set up,and the difference dynamic behavior of the friction-induced and harmonically-forced vibration system is researched by Runge-Kutta.The sticking and sliding periodic vibration and the bifurcation characteristics presented with increasing or decreasing the exciting frequency of this vibration system are revealed.The influence of the clearance value on the periodic impact vibration,bifurcation and sliding-sticking phase of the system is analyzed.The result shows that the dynamic behavior of this vibration system becomes easier and the frequency window of the sticking periodic vibration becomes narrower with the increase of clearance.
A two-degrees-freedom vibration system with two clearances and dry friction is set up,and the difference dynamic behavior of the friction-induced and harmonically-forced vibration system is researched by Runge-Kutta.The sticking and sliding periodic vibration and the bifurcation characteristics presented with increasing or decreasing the exciting frequency of this vibration system are revealed.The influence of the clearance value on the periodic impact vibration,bifurcation and sliding-sticking phase of the system is analyzed.The result shows that the dynamic behavior of this vibration system becomes easier and the frequency window of the sticking periodic vibration becomes narrower with the increase of clearance.
引文
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[2]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,2014,33(3):41-45.
[3]IVANOV A P.Stabilization of an impact oscillator near grazing incidence owing to resonance[J].Journal of Sound and Vibration,1993,162(3):562-565.
[4]HU H Y.Detection of grazing orbits and incident bifurcations of a forced continuous,piecewise-linear oscillator[J].Journal of Sound and Vibration,1994,187(3):485-493.
[5]XIE J H.Codimension two bifurcations of an impacting vibrating system[J].Applied Mathematics and Mechanics,1996,17(1):65-75.
[6]罗冠炜,谢建华,孙训方.具有单侧刚性约束的两自度振动系统在强共振条件下的拟周期运动与混沌[J].固体力学学报,2000,21(2):138-144.
[7]SOUZA S L T D,CALDAS I L.Controlling chaotic orbits in mechanical systems with impacts[J].Chaos,Solitons and Fractals,2004,19:171-178.
[8]JIN D P,HU H Y.Periodic vibro-impacts and their stability of a dual component system[J].Acta Mechanica Sinica,1997,13(4):366-376.
[9]SOUZA S L T D,CALDAS I L.Calculation of Lyapunov exponents in systems with impacts[J].Chaos Solitons&Fractals,2004,19(3):569-579.
[10]PETERKA F.Bifurcation and transition phenomena in an impact oscillator[J].Chaos,Solitons and Fractals,1996,7(10):1635-1647.
[11]罗冠炜,谢建华.碰撞振动系统的周期运动与分岔[M].北京:科学出版社,2004:1.