This paper proposes a unified approach to establish the analytical vibro-acoustic coupled model consisting of the tensioned membrane and the closed cavity. A 2-D Fourier cosine series with auxiliary functions is used to derive the displacement of the membrane structure. The sound pressure inside the cavity is expressed as a 3-D Fourier series with additional terms by the method of wave acoustics. Then, the vibro-acoustic coupled model between the membrane and the closed cavity is established based on the Hamilton's principle, which is suitable for different boundary conditions. The program developed by this method can be used to study the sound radiation power and sound transmission loss of coupled systems with various parameters. To demonstrate the accuracy of the proposed method, the free and forced responses of the coupled model are compared with results obtained by finite element method. The membrane with general boundary conditions is well investigated. Besides, the acoustic characteristics of the coupled model are analyzed by adjusting membrane thickness, membrane tension, cavity depth, membrane mounting position and source position, including sound radiation power and sound transmission loss. And the findings have been interpreted appropriately.

本文提出了一种统一的方法来建立由张拉膜和封闭腔组成的解析振动声耦合模型。具有辅助功能的二维傅里叶余弦级数用于推导膜结构的位移。空腔内的声压通过波声学方法表示为带有附加项的 3-D 傅里叶级数。然后，基于哈密顿原理建立了膜与封闭腔之间的声振耦合模型，该模型适用于不同的边界条件。该方法开发的程序可用于研究各种参数耦合系统的声辐射功率和声传输损耗。为了证明所提出方法的准确性，将耦合模型的自由和受迫响应与有限元法得到的结果进行了比较。对具有一般边界条件的膜进行了很好的研究。此外，通过调整膜厚、膜张力、腔深、膜安装位置和声源位置，分析耦合模型的声学特性，包括声辐射功率和声传输损耗。并且这些发现得到了适当的解释。