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Journal of Vibration and Control
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Optimal Design of Shape Memory Alloy Damper for Cable Vibration Control

Xiao-Bao Zuo

Department of Civil Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, P.R.China, xbzuo{at}sina.com

Ai-Qun Li

College of Civil Engineering, Southeast University, Nanjing Jiangsu Province 210096, P.R.China

Wei Sun

Jiangsu Key Lab of Construction Materials, Southeast University, Nanjing Jiangsu Province 210089, P.R.China

Xiang-Hua Sun

School of Science, Nanjing University of Science and Technology

In order to apply shape memory alloy (SMA) damper for effective control of cable vibration under external excitations, motion equations and corresponding state equation of the system made up of SMA dampers and a cable are described based on Hamilton Principle, and the system's optimization problems based on the linear quadratic regulator (LQR) active control algorithm are investigated to obtain the optimum cable vibration control effects and control forces. According to the equivalency between SMA damper optimum passive control effects and LQR active control effects, the optimal design principle and methods of SMA damper for cable vibration control are proposed. Utilizing the above optimal methods, a SMA damper is designed to control vibration of a practical cable under white noise excitations, and its control effects are compared with the LQR active control effects by numerical simulation. Results show that the cable vibration responses under both LQR active control and SMA damper optimum control are obviously less than those without control, and SMA damper optimum control effects are approached to the LQR active control effects. This may indicate the effectiveness of the supposed SMA damper optimum design methods for cable vibration control.

Key Words: Cable vibration control • SMA damper • optimal design • equivalence with LQR active control.

This version was published on June 1, 2009

Journal of Vibration and Control, Vol. 15, No. 6, 897-921 (2009)
DOI: 10.1177/1077546308094916
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