小垂度粘弹性索非线性响应及振动主动控制

李映辉; 高庆; 殷学纲

小垂度粘弹性索非线性响应及振动主动控制

1.
西南交通大学, 应用力学与工程系, 成都, 610031;
2.
重庆大学工程力学系, 重庆, 400044

基金项目: 国家自然科学基金资助项目(5936140);国家教委博士点基金资助项目;航空工业总公司基金资助项目

详细信息

作者简介:
李映辉(1964- ),男,四川南江人,博士,副教授(E-mail:li-yinghui@sina.com)

中图分类号: TU501;TU511.3⁺2
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- 文章访问数: 2287
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- 被引次数: 0
出版历程
- 收稿日期: 2002-05-18
- 修回日期: 2003-01-06
- 刊出日期: 2003-05-15

Nonlinear Dynamic Response and Active Vibration Control of the Viscoelastic Cable With Small Sag

1.
Deptartment of Applied Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.China;
2.
Deptartment of Engineering Mechanics, Chongqing University, Chongqing 400044, P.R.China

摘要

摘要: 研究具有初始应力的小垂度粘弹性索的非线性动态响应及振动主动控制。在假定索材料的本构关系为一般微分本构类型的基础上,建立小垂度粘弹性索的运动微分方程;应用Galerkin方法将其转化为可用Runge-Kutta数值积分方法求解的一系列三阶非线性常微分方程。在仅考虑面内的横向振动及忽略非线性的情况下得到了连续状态空间中的状态方程,将状态方程离散为差分方程形式,并用矩阵指数来逐步近似状态转移矩阵;基于二次性能指标的最小化得到了最优的控制力与状态向量。最后通过数值仿真研究说明了粘性参数对索动态响应的影响。
- 小垂度粘弹性索 /
- Revlon材料 /
- 动力响应 /
- 振动主动控制
Abstract: The problem considered is an initially stressed viscoelastic cable with small sag.The cable material is assumed to be constituted by the hereditary differential type.The partial differential equations of motion is derived first.Then by applying Galerkin.s method,the governing equations are reduced to a set of third order non-linear ordinary differential equations which are solved by Runge-Kutta numerical integration procedures.Only after the transverse vibration of the plane is considered and the nonlinear terms are neglected,can the non-linear ordinary differential equations be expressed as a continuous state equation in the state space.The matrix of state transition is approximated stepwise by the matrix exponential;in addition,the state equation is discretized to a difference equation to improve the computing efficiency.Furthermore,an optimal control of procedure system based on the minimization of a quadratic performance index for state vector and control forces is developed.Finally,the effect of dynamic response of the cable,which is produced by viscoelastic parameters,is testified by the research of digital simulation.
- viscoelastic cable /
- Revlon material /
- dynamic response /
- active vibration control

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参考文献(11)

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