Superposition of frequency-independent normal modes in exterior acoustics

The radiated sound power of sound sources has to be determined under free-field conditions in order to neglect reflections at surrounding walls. This also applies for the numerical simulation of sound radiation. Different numerical approaches as the boundary element method or perfectly matched layers are commonly used in order to deal with non-reflective exterior computational domains. However, harmonic analysis requires inversion of frequency-dependent matrices for each frequency of interest separately. The authors use the concept of normal modes for sound sources in unbounded computational domains by application of the Astley-Leis infinite element method. The system matrices do not depend on the frequency and so do the normal modes, which can be found as eigenvalues and eigenvectors of a single, linearized quadratic eigenvalue problem. The computational effort can be reduced if the modal basis is reduced. A reduced number of normal modes is superimposed and the radiated sound pressure and power can be predicted with a sufficient accuracy. The investigations in this work aim at development of a priori criteria for distinction of relevant and negligible normal modes. Since only one single eigenvalue problem has to be solved and due to the fact that the modes do not depend on the load case, the computational effort might be reduced significantly compared to harmonic analysis.