一类准周期参激非线性扭振系统的周期簇发

时培明;;李纪召;刘彬; 韩东颖

振动与冲击 ›› 2012, Vol. 31 ›› Issue (4) : 100-104,.

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PDF(882 KB)
振动与冲击 ›› 2012, Vol. 31 ›› Issue (4) : 100-104,.
论文

一类准周期参激非线性扭振系统的周期簇发

  • 时培明1, 2 ; 李纪召1 ; 刘彬1; 韩东颖3
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Periodic bursting of a nonlinear torsional vibration system under quasic-periodic parametric excitation

  • SHI Pei-ming1,2; LI Ji-zhao1; LIU Bin1; HAN Dong-ying3
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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

Abstract

Considering the effects caused by the coexist of two different periodic parametric excitation in rotary machinery driving system, the dynamical equation of nonlinear torsional vibration system is 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 are obtained by solving the torsional vibration system using multi-scale method. On this basis, the periodic bursting of the nonlinear torsional vibration system is studied when the two periodic parametrical excitations have large difference gap. The influence of fast-varying parametrical excitation and slow-varying parametrical excitation on the periodic bursting of the torsional vibration system is analyzed. The parameter regions of periodic bursting are given by numerical simulation. The mutual transition between the quiescent state and the spiking state of the system occurs in this region, when the amplitude of the fastly varying excitation reduces, the area of spiking state extends, the time of bursting prolongs. The bursting type and trajectory of the system can be changed from regulating amplitude of slow-varying parametric excitation.

关键词

旋转机械 / 准周期参激 / 扭振 / 周期簇发

Key words

rotating machinery / quasic-periodic parametric excitation / torsional vibration / periodic bursting

引用本文

导出引用
时培明;;李纪召;刘彬; 韩东颖. 一类准周期参激非线性扭振系统的周期簇发[J]. 振动与冲击, 2012, 31(4): 100-104,
SHI Pei-ming;LI Ji-zhao; LIU Bin; HAN Dong-ying. Periodic bursting of a nonlinear torsional vibration system under quasic-periodic parametric excitation[J]. Journal of Vibration and Shock, 2012, 31(4): 100-104,

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