Research On Theory And Algorithm Of Local Vibration Control Of Structure

There are two ways for local vibration control of structure: the passive control and active control. Since the passive control is easy for the engineering realization, it gains more attention in engineering field. Now, theory research and engineering practice of the passive control have been well-developed. As for the active control of structure, it has already arrived at the stage of intelligent-structrue control. One of main questions in the active control concerns with pole assignment or modal control.As we know, the one of main objective of system control is modal control. We can control both part of modes and the whole modes. But the condition is the respective modes are controllable. So controllability problem plays a key role in vibration control and suppression of a vibration system. In this dissertation two necessary conditions of completely controllability of a repeated eigenvalues system (regular and defective system) and its proof are given. At same time two sufficient conditions and its proof are also presented. According to above theory, this dissertation gives a method of selecting control force distribution matrix and some numerical example.About pole assignment of system it is still an open question. There is not a sufficient and necessary condition to answer that some poles are assignable, and some others are not to any control system. Poles replacement is one of important goal of system control. Now using feedback control to assign poles is one of main pole assignment method. There are two kinds of feedback control, one is state feedback control and another is output feedback control. In this dissertation, modal computing method of output feedback control gain matrix in pole assignment problem is addressed by using modal coordinates. It is obvious advantage to save computing time and protect some methods from invalidity for high order structure. The numerical example of a cantilever beam is presented. The output feedback gains are computed by using original structural state space equation, four-order, six-order and eight-order state space equation of modal coordinates for first two eigenvalue assignment of original structure, respectively, and then apply those gains obtained under modal coordinates to original structural state space equation. Comparing the control effect of Modal gains with one of original gain, it is verified that modal computing method is available.By combining the orthogonality relations for a symmetric definite quadratic pencil and the open-loop eigenvector orthogonal projection, an effective method is formed to deal with the partial poles assignment. The method can assign some poles and corresponding eigenvectors of a given structure, while leave the other eigenpairs unchanged. Moreover, this orthogonal projection method makes the assigned closed-loop eigenvector as close as possible to the original open-loop eigenvector and this leads the closed-loop system has the similar behavior as the open-loop system. After properly selecting the open-loop eigenvectors which are corresponding to the repeated poles, we can also use the method to assign repeated poles. Finally, two numerical examples are presented to illustrate the validity of the method.This paper also discusses the theory and applications of the receptance method in the local vibration control of structure. Through this method, the vibration control can be realized without acquirement of the approximate mathematical model of the structure.