摘要
考虑旋转机械中两种频率不同的周期参数激励同时存在对其传动系统的影响,基于拉格朗日方程,建立一类含准周期参激刚度和摩擦阻尼的非线性扭振系统的动力学方程。运用多尺度法对该扭振系统进行求解,得到系统在1/2亚谐波主参数共振下的幅频特性方程和分岔响应方程。在此基础上,研究了当两种周期参激的频率相差较大时非线性扭振系统的周期簇发现象,分析了快变参激和慢变参激对扭振系统的周期簇发的影响。通过数值仿真,给出了产生周期簇发的参数取值区域。在该区域内系统发生静息态与激发态的相互转迁,当快变激励的幅值减小时,激发态区域扩大,簇发的时间延长,通过调节慢变参激幅值会改变系统簇发的类型和轨迹。
Considering the effects caused by the coexisting of two different periodic parametric excitations in rotating machinery driving system,the dynamical equation of a nonlinear torsional vibration system was established based on Lagrange equation.The model contains quasi-periodic parametrically excited stiffness and friction damping.The amplitude-frequency characteristic equation and bifurcation response equation were obtained by solving the torsional vibration system using multi-scale method.On this basis,the periodic bursting of the nonlinear torsional vibration system was studied when large difference gap exists between the frequencies of the two periodic parametrical excitations.The influences of fast-varying parametrical excitation and slow-varying parametrical excitation on the periodic bursting of the torsional vibration system were analyzed.The parameter regions of periodic bursting were obtained with the help of numerical simulation.The mutual transition between quiescent state and spiking state of the system occurs in this region.When the amplitude of the fast-varying excitation reduces,the area of spiking state extends and the time of bursting prolongs.The bursting type and trajectory of the system can be changed by regulating the amplitude of slow-varying parametric excitation.
出处
《振动与冲击》
EI
CSCD
北大核心
2012年第4期100-104,共5页
Journal of Vibration and Shock
基金
国家自然科学基金项目(51005196)
河北省自然科学基金项目(F2010001317
E2010001262)
秦皇岛市科学技术研究与发展计划项目(201001A085)
关键词
旋转机械
准周期参激
扭振
周期簇发
rotating machinery
quasic-periodic parametric excitation
torsional vibration
periodic bursting
