Optimal Design of Shape Memory Alloy Damper for Cable Vibration Control

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.