THE APPROXIMATE SOLVING METHOD OF THE CABLES NONLINEAR CONTROL SYSTEMS - LI JianQiang; WANG XiuYong; SUN HongXin (Jixie qiangdu)
The large amplitude transverse vibration of stay cable on the cable-stayed bridges will be caused easily under external excitations,and the method by applying an axial control force to mitigate the transverse vibration was proved to be feasible. Due to the effect of axial force,the cable vibration control system has nonlinear features,which will result in the complicated and difficult solution. In this paper,the nonlinear discrete time control system model of the cable is established. The average linearization and the initial value linearization method were proposed according to bilinear characteristics of system control matrix,and the vibration reduction effect of linearization method has been analyzed theoretically. Taking the first three modal control system of the cable as an example,the simulation of vibration reduction effect was carry out. The results show that the vibration reduction effect of the proposed linearization methods is 5% lower than that of the nonlinear methods,and can also achieve good damping effect,and the mitigating effect of the two linearization methods are basically the same under the free vibration and random excitation.