基于左特征向量配置的结构声主动控制

摘要

The left eigenvectors of a closed loop system were controlled to be orthogonal with the excitation force vector for the active structural acoustic control by use of the dependent modal space control (DMSC) method.The relationship between the left eigenvectors and the mode shapes of the vibration system was derived.The conclusion was drawn that the left eigenvectors of the closed loop system are also a linear combination of the left eigenvectors of its corresponding open loop system when the mode shapes of the closed loop system are a linear combination of the mode shapes of the open loop system.The left eigenvectors orthogonal with excitation force vector were constructed and the mode shapes corresponding to the constructed left eigenvectors were considered as the control target,then the control of the left eigenvectors of the closed loop system was realized by the DMSC method indirectly,and finally the active structural acoustic control was achieved.The active structural acoustic control method proposed has the characteristics of clear physical meaning,simple implementation and good sound radiation control performance.The active structural acoustic control of a rectangular simply supported plate was numerically evaluated,and the first and fourth left eigenvectors of the closed loop system were assigned to be orthogonal with the excitation force vector by the DMSC method.The results show that the control scheme proposed here is very efficient in reducing sound radiation.%结合耦合模态空间控制方法通过配置闭环系统的左特征向量实现了结构振动声辐射的主动控制.推导了振动系统的左特征向量与模态振型之间的关系,得出了当闭环系统的模态振型为开环系统的模态振型的线性组合时,闭环系统的左特征向量也为开环系统的左特征向量的线性组合的结论.构造了与激励力向量正交的目标左特征向量,以该左特征向量对应的模态振型为控制目标,采用耦合模态空间控制方法,间接实现了对闭环系统的左特征向量的配置,最终实现了结构振动声辐射的主动控制.提出的结构声主动控制方法具有物理意义明确、实施过程简单、声辐射控制效果好的特点.文中以矩形简支板为例进行了结构声辐射主动控制仿真,将闭环系统的第1、4阶左特征向量配置成与激励力向量正交的形式.仿真结果表明简支板的结构振动声辐射得到了有效降低.