Analytical coupled vibro-acoustic modeling of tensioned membrane backed by the rectangular cavity

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.