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

Abstract

When using the finite element method (FEM) for a structural-acoustic coupled analysis, the mass and stiffness matrices are not symmetric because the acoustic space is described by sound pressure and the structure is described by displacement. Therefore, eigenvalue analysis takes a long time. In our previous studies, we have proposed a concentrated mass model for in performing structural-acoustic coupled analysis. The advantage of this model is that the mass and stiffness matrices become symmetric because both the acoustic space and the membrane are described by the displacement of the mass points. However, some physically meaningless modes, such as spurious modes and zero eigenvalues, arise with this model. In this paper, we propose a new concentrated mass model that does not generate the spurious modes and zero eigenvalues. This model can be used to analyze a coupled system of a two-dimensional acoustic space and a membrane. The mass points of the new model are placed at the sides of elements rather than at nodal points. To confirm the validity of the proposed model, the natural frequency obtained by using the concentrated mass model is compared with the natural frequency found by using FEM. These results are in good agreement, and spurious modes and zero eigenvalues are not generated in the proposed model. Furthermore, we compared the proposed model with FEM in terms of the time required for the eigenvalue analysis. Because the mass and stiffness matrices of the proposed model are symmetric, its eigenvalue analysis is faster than that of FEM, whose matrices are asymmetric. Therefore, we conclude that the proposed model is valid for coupled analysis of a two-dimensional acoustic space and membrane vibration, and that it is superior to FEM in terms of calculation time.