非线性梁结构的参数振动稳定性及其主动控制

李凤明; 刘春川

doi:10.3879/j.issn.1000-0887.2012.11.004

非线性梁结构的参数振动稳定性及其主动控制

doi: 10.3879/j.issn.1000-0887.2012.11.004

李凤明^1,2,,
刘春川²

北京工业大学机电学院, 北京 100124;

基金项目: 国家自然科学基金资助项目(11172084；10672017；50935002)

详细信息

通讯作者:
李凤明(1969—),男,黑龙江人,教授,博士,博士生导师(联系人.Tel:+86-451-86414479;E-mail:fmli@hit.edu.cn).

中图分类号: O322；O317
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- 被引次数: 0
出版历程
- 收稿日期: 2011-08-27
- 修回日期: 2012-06-17
- 刊出日期: 2012-11-15

Parametric Vibration Stability and Active Control of Nonlinear Beams

LI Feng-ming^{1,2
,},
LIU Chun-chuan²

¹College of Mechanical Engineering, Beijing University of Technology,Beijing 100124, P.R.China;²School of Astronautics, Harbin Institute of Technology, P.O.Box 137, Harbin 150001, P.R.China

摘要

摘要: 采用压电材料研究了参数激励非线性梁结构的运动稳定性及其主动控制，通过速度反馈控制算法获得主动阻尼，利用Hamilton原理建立含阻尼的立方非线性运动方程，采用多尺度方法求解运动方程获得稳定性区域．通过数值算例，分析了控制增益、外激振力幅值等因素对稳定性区域和幅频曲线特性的影响．分析表明：控制增益增大，结构所能承受的轴向力也增大，在一定范围内结构的主动阻尼比也增加；随着控制增益的增大，响应幅值逐渐降低，但所需的控制电压存在峰值点．
- 梁 /
- 压电材料 /
- 参数振动 /
- 稳定性 /
- 主动控制 /
- 多尺度法
Abstract: The vibration stability and active control of the parametrically excited nonlinear beam structures were studied using the piezoelectric material. The velocity feedback control algorithm was applied to obtain the active damping. The cubic nonlinear equation of motion with damping was established by employing Hamilton’ principle. The method of multiple scales was used to solve the equation of motion, and the stable region was obtained. The effects of the control gain and amplitude of the external force on the stable region and amplitudefrequency curve characteristics were analyzed numerically. From the numerical results it was seen that with the increase of the feedback control gain, the axial force to which the structure could be subjected increased, and in certain scope the structural active damping ratio also increased. With the increase of the control gain, the response amplitude decreases gradually, but the required control voltage exists peak value.
- beam /
- piezoelectric material /
- parametric vibration /
- stability /
- active control /
- method of multiple scales

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参考文献(19)

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