A comparison of acoustic radiation modes and frequency-independent normal modes in acoustic exterior problems

The acoustic radiation efficiency and the sound power are suitable quantities to describe the entirely radiated sound from vibrating structures. Both can be calculated by modal superposition of those eigenvectors of the system matrices that are associated with the boundary of the structure. The respective matrices are obtained by using numerical methods. The surface velocities of a solid structure, which is acting as a sound source, yield the boundary conditions of its surrounding fluid that is calculated by using the Finite Element Method (FEM). Infinite Elements or Perfectly Matched Layers (PML) provide appropriate radiation decay behaviour for the exterior problem. In this paper, two different types of acoustic exterior modes are investigated and compared to each other for two-dimensional problems. On the one hand, the eigenvectors of the real and symmetric coupling matrix form an orthogonal basis of the frequency-dependent acoustic radiation modes. On the other hand, the normal modes, which can be obtained as eigenvectors from the state-space system matrices of the quadratic eigenvalue problem, are independent of frequency. Considering the issue of the contribution of single mode shapes to the total superimposed sound power, the applicability of modal reduction is discussed.