Analytical model of vibro-acoustic coupling between the membrane loaded with concentrated masses and the acoustic cavity

Abstract

In this paper, sound radiation and sound transmission characteristics of a membrane-cavity system loaded with concentrated masses are analyzed. The Fourier cosine series function with additional terms is used as the mode function of membrane to model the single membrane structure, which is suitable for arbitrary boundary conditions. The concentrated masses are regarded as the concentrated mass points without considering their sizes, and the coupling structure of membrane and mass blocks is constructed. The structure-sound field fully coupled model is also constructed by using the energy principle and Rayleigh–Ritz method. Several numerical examples computed by finite element method are used for verification. The influence of the added mass blocks on the membrane modes and acoustic properties of the coupling system is discussed, including membrane parameters, mass block arrangement, quantity and mass, etc. Also, the mass blocks are dispersed for analysis. Results show that dispersing the mass can significantly increase the frequency of the coupling mode between the membrane and concentrated masses and better suppress the vibration. But increasing dispersion points does not further enhance vibration suppression. Instead, it expands the area where the membrane vibrates violently.