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为度量密频结构中密集模态组内各模态之间的相关度,定义了模态相关准则,阐述了结构系统具备一定条件时会出现模态频率集聚及对应模态相关度高的特性.在此基础上,通过可控/可观性Gram阵的分块解析形式,分析了作动器/传感器的配置方式对模态相关度高的密集模态组内各模态可控/可观度的影响,据此简化了基于模态可控/可观度准则的元件优化配置问题.此外,证明了密频组模态相关度高时,独立模态控制中可降低控制/观测向量的维度,即减少作动器/传感器的数目,在不损失性能的前提下实现对密频组的降维控制.最后通过算例仿真证明,对包含强相关性密集模态的结构,基于本文理论可简化作动器/传感器的配置问题,并且根据本文理论设计的低阶降维控制系统可实现对结构有效的振动抑制。
In order to measure the correlation between modalities in a dense modal group in a dense-frequency structure, the modal correlation criterion is defined, and the characteristics of modal frequency clustering and corresponding modal correlations are presented when the structural system has certain conditions On the basis of the analysis of the block / parse form of the controllable / observability Gram matrix, we analyzed the controllability / observability of each mode in the dense modal group with high modal correlation between actuator and sensor configuration , Which simplifies the optimization of component placement based on the modal controllable / observability criterion.In addition, it is proved that the dimensionality of the control / observation vector can be reduced in the independent modal control when the modal correlation of the dense-frequency group is high, That is to reduce the number of actuators / sensors and to realize the dimensionless control of the dense-frequency group without loss of performance.Finally, a numerical simulation is given to show that the structure containing strongly-dependent dense modes can be simplified based on the theory of this paper Actuator / sensor configuration problems, and the low-order dimension control system designed according to the theory of this paper can achieve effective structural vibration suppression.