Coupled analysis of two-dimensional acoustic and membrane vibration by concentrated mass model

In the finite element method of a structural-acoustic coupled analysis, the mass matrix and the stiffness matrix are not symmetrical. Therefore, the modal analysis cannot be applied directly to the coupled problem. In our previous study, a concentrated mass model was proposed to analyze a two-dimensional acoustic analysis. The model consists of the masses, the connecting springs. It is very easy to couple the structure and acoustic field by the concentrate mass model. Furthermore, the mass matrix and the stiffness matrix are symmetrical. In this paper, we propose a concentrated mass model to perform a coupled analysis of a two-dimensional acoustic and a membrane vibration. And we propose a coupling method to arrange of the masses of the air near the membrane. To confirm the validity of the proposed model, the natural frequency obtained by the concentrated mass model is compared with the natural frequency by the modal coupling method. These results are in good agreement. Therefore, it is concluded that the proposed model is valid for the coupled analysis of an acoustic and a vibration analysis.