The Actuating Equation Of Macro Fiber Composite And Its Active Control Of Stayed Cable Vibration

With the rapid development of traffic,our country has built more and more long-span bridges to facilitate people to pass.Due to their excellent spanning capabilities,Cable-stayed bridges have become one of the major long-span bridge structures today.As one of the main components of the cable-stayed bridge,the stayed cables play the role of load bearing and force transmission.Because the stayed cable is a small damping structure with high flexibility and light weight,it can easily generate various forms of vibration under external load.The long-term vibration will cause the anchorage end of the cable to fatigue and even damage.The redistribution of the internal forces of the bridge structure will result in damage to the bridge structure under severe circumstances,causing huge economic losses.In order to suppress the vibration of stayed cable,passive or semi-active control methods are usually adopted in the project,but they all have certain defects.For this reason,macro fiber composite?MFC?is introduced as the vibration control device for the stayed cables.As a new type of piezoelectric smart material,macro fiber composite?MFC?is composed of piezoelectric ceramic fiber,epoxy resin base,and interdigitated electrode.It has extremely light weight,good flexibility,good actuating effect,and wide actuating frequency range and other advantages.At present,MFC has been applied to the field of vibration control of plate and shell structure.However,there are few researches on the actuating performance of MFC at home and abroad.A complete set of coupled actuating equation of MFC and controlled structures has not yet been developed.Therefore,the paper studies the coupled actuating equation of MFC and controlled structure,establishes two actuating equations of MFC,completes the actuating test of MFC on plate structure;This paper presents a vibration reduction method for stayed cables based on MFC.The control method used is active control method,and the vibration control simulation of stayed cables are carried out.The main work of this paper is as follows:1)The two actuating equations of macro-fiber composite were deduced,and the effects of Poisson's ratio and Poisson's ratio of MFC on the actuating force of MFC were discussed.The MFC's plate actuating simulation and test are conducted,and the applicability of the two actuating equations of macro-fiber composite is analyzed and verified.2)An additional bending moment of stayed cable for vibration reduction method based on MFC is proposed.The MFC is affixed axially symmetrically along the stayed cable,so that the MFC exerts additional bending moment on the cable.The additional bending moment provided by the MFC is equivalent to the distribution force perpendicular to the stayed cable,and the dynamic equation of the stayed cable is established.3)The model reduction method of the balanced truncation model and the H₂ norm reduction method are used to reduce the order of the stayed cable model.The results of the two methods are compared,and the vibration control simulation is carried out by using the results of the balanced truncation model.4)The PID control method and Fuzzy-PID control method are used to simulate the active control of the stayed cable model.The results show that the Fuzzy PID control method is more effective,which shows that the MFC control of the cable-stayed cable vibration is feasible.