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

LI Ying-hui; GAO Qing; YIN Xue-gang

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Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(5): 529-536

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, 2003, 24(5): 529-536.

Citation:

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, 2003, 24(5): 529-536.

Citation:

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, 2003, 24(5): 529-536.

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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

Received Date: 2002-05-18
Rev Recd Date: 2003-01-06
Publish Date: 2003-05-15

Abstract

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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References(11)

References

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