NONLINEAR DYNAMIC RESPONSE AND ACTIVE VIBRATION CONTROL OF THE VISCOELASTIC CABLE WITH SMALL SAG

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (5): 596-604.

NONLINEAR DYNAMIC RESPONSE AND ACTIVE VIBRATION CONTROL OF THE VISCOELASTIC CABLE WITH SMALL SAG

李映辉¹, 高庆¹, 殷学纲²

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

收稿日期:2002-05-18 修回日期:2003-01-06 出版日期:2003-05-18 发布日期:2003-05-18
基金资助:
the National Natural Science Foundation of China(59635140); the Doctoral Point Foundation of Education Ministry in China

NONLINEAR DYNAMIC RESPONSE AND ACTIVE VIBRATION CONTROL OF THE VISCOELASTIC CABLE WITH SMALL SAG

LI Ying-hui¹, GAO Qing¹, YIN Xue-gang²

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

Received:2002-05-18 Revised:2003-01-06 Online:2003-05-18 Published:2003-05-18
Supported by:
the National Natural Science Foundation of China(59635140); the Doctoral Point Foundation of Education Ministry in China

摘要/Abstract

摘要： 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 nonlinear 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 nonlinear 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.

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 nonlinear 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 nonlinear 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.

中图分类号:

李映辉;高庆;殷学纲. NONLINEAR DYNAMIC RESPONSE AND ACTIVE VIBRATION CONTROL OF THE VISCOELASTIC CABLE WITH SMALL SAG[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(5): 596-604.

LI Ying-hui;GAO Qing;YIN Xue-gang. NONLINEAR DYNAMIC RESPONSE AND ACTIVE VIBRATION CONTROL OF THE VISCOELASTIC CABLE WITH SMALL SAG[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(5): 596-604.

参考文献

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[7] Fung R F, Huang J S, Cheng Y, et al. Nonlinear dynamic analysis of the viscoelastic string with a harmonically varying transport speed[J]. Computers & Structures, 1996,61(1): 125-132.
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NONLINEAR DYNAMIC RESPONSE AND ACTIVE VIBRATION CONTROL OF THE VISCOELASTIC CABLE WITH SMALL SAG

NONLINEAR DYNAMIC RESPONSE AND ACTIVE VIBRATION CONTROL OF THE VISCOELASTIC CABLE WITH SMALL SAG

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