2016 年 82 巻 836 号 p. 15-00584
Some acoustic problems such as interior noise analysis of vehicles need to be treated as structural-acoustic coupled problems because the coupling effect cannot be ignored. To solve such problems, the finite element method (FEM) has been used. However, the acoustic space is described by sound pressure and the structure is described by displacement. Therefore, the mass matrix and stiffness matrix of FEM are asymmetric, and it takes a long time to conduct eigenvalue analysis. In our previous studies, we proposed a concentrated mass model to perform acoustic analysis. In this study, we propose a concentrated mass model to analyze a coupled system of two-dimensional acoustic space and a membrane. This model consists of mass points and connecting springs. The advantage of this model is that the mass matrix and stiffness matrix are symmetric because both the acoustic space and the membrane are described by the displacement of the mass points. We conducted eigenvalue analysis and compared the proposed model with FEM. There are some modes such as spurious modes and zero-frequency modes that are physically meaningless. However, excepting these modes, the eigenvalue analysis result obtained using the proposed model agrees with the natural frequencies and natural modes obtained by FEM. Moreover, the eigenvalue analysis result becomes more accurate as the mass points of the acoustic space are placed closer to the mass points of the membrane because the boundary conditions are satisfied. Furthermore, we compared the proposed model with FEM in terms of the time required for the eigenvalue analysis. Because the mass matrix and stiffness matrix of the proposed model are symmetric, its eigenvalue analysis is faster than that of FEM, whose matrixes are asymmetric. Therefore, we conclude that the proposed model is valid for the coupled analysis of two-dimensional acoustic space and membrane vibration and is superior to FEM in terms of calculation time.
