Coupled analysis of two-dimensional acoustic and membrane vibration by concentrated mass model: Proposal of spurious mode elimination model

When using the finite element method for 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 requires a long computational time. In this article, we proposed concentrated mass models for 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. Furthermore, our models do not generate spurious modes and zero eigenvalues that arise in finite element method whose variable is displacement in acoustic space. To validate the proposed models, the natural frequency obtained using the concentrated mass models is compared with the natural frequency found using finite element method. These results are in good agreement, and spurious modes and zero eigenvalues are not generated in the proposed model whose variables are sound pressure. Furthermore, we compare the proposed model with finite element method in terms of the calculation time required for the eigenvalue analysis. Because the matrices of the proposed models are symmetric, these eigenvalue analyses are faster than that of finite element method, 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 finite element method in terms of calculation time.