智能结构密频系统振动控制及其摄动分析

VIBRATION CONTROL AND PERTURBED ANALYSIS OF INTELLIGENT STRUCTURES WITH CLOSELY-SPACED EIGENVALUES

提出一种智能结构密频系统振动控制规律的设计方法．其主要工作为：将密频子空间转 化为重频子空间，把密频系统作为重频系统上的摄动；为了解决重频密频子空间相对应的特征 向量选取的敏感性问题，通过摄动分析得到与重频密频子空间相对应特征向量的线性组合并利 用闭环系统特征值极点配置的方法得到重频密频系统的振动控制规律；把所设计的振动控制规 律作用于原系统和摄动系统上，讨论了结构参数改变后对系统的动态特性的影响；最后通过算 例证明该方法的有效性．

If small changes of structural parameters of intelligent structures with closely-spaced eigenvalues are made, eigenvectors corresponding to multiple eigenvalues may have a jump that may not be small. The reason arising the jump of the eigenvectors is that eigenvectors corresponding to multiple eigenvalues are not unique. It is very difficult for the method that deals with vibration control of structures with distinct eigenvalues not to be used to solve vibration control of structures with repeated or closely-spaced eigenvalues.So a method to design the vibration control law of intelligent structures with closely-spacedeigenvalues is presented in this paper. The active control of the intelligent structures with closely-spaced eigenvalues is studied to include four aspects: firstly, the system with closely-spaced eigenvalues is transformed into that with repeated eigenvalues by the spectral decomposition method; secondly the linear combination of eigenvectors corresponding to repeated eigenvalues is obtained by the perturbation method of systems with repeated eigenvalues;thirdly, the vibration control law is designed on the basis of the system with repeated eigenvalues; finally, if the vibration control law is applied to the original system and perturbed system, the 1st order perturbations are discussed when the small parameter modifications of the system are introduced. A numerical example is given to demonstrate the application of the present method.