中文摘要：

通过辐射模态研究了封闭空间的结构声辐射及其有源控制问题．分析了辐射模态的数学和物理意义并揭示了辐射模态与声腔模态之间的内在耦合关系，并通过声辐射模态建立了弹性封闭空间结构声辐射有源控制模型．针对辐射模态在有源控制中的应用实现问题，给出了一种新的控制策略，即将辐射模态按对应辐射效率或耦合强度从大到小排列，使前k阶声辐射模态声势能最小化．采用压电陶瓷作动器作为控制力源进行了封闭空间结构声辐射有源控制数值计算与分析研究．结果表明，辐射模态与声腔模态的耦合具有严格的选择性，各阶辐射模态的形状和与相耦合的主导声模态在耦合面上的形状非常相似；在低频范围内，一般只需最小化前三阶辐射模态声势能，在更低频或声模态频率附近，只需最小化前一阶最有效辐射模态声势能，便能和总声势能最小化策略控制效果基本一样．

英文摘要：

Acoustic radiation modes of the flexible boundary of an enclosure were obtained using eigenvalue decomposition based on the quadratic form of total time-averaged acoustic potential energy. The physical characteristics of the radiation modes and the inherent relationships between the cavity modes and the radiation modes were analyzed. A model for the active control of sound radiation from a vibrating structure into an enclosure was presented based on radiation mode sensing and the use of Pb zirconate titanate （PZT） piezoelectric actuators. According to the characteristics of the radiation modes, a new control strategy was developed： modal acoustic potential energies corresponding to the first radiation modes were minimized after the radiation modes were ranked in descending order. Numerical simulations and analyses with the proposed strategy were conducted. The results showed the coupling between radiation modes and cavity modes is strictly selected; the radiation mode shape is very similar to the projection on the coupling surface of the coupled main cavity~ mode. In the low frequency range, generally the first three modal acoustic potential energy needs to be minimized, however, at the modal frequency of the cavity or a very low frequency, only the modal acoustic potential energy corresponding to the previous most efficient radiation mode needs to be minimized. Finally the mechanisms involved in PEM were analyzed from the point of view of the radiation modes.