Trapped eigenmodes and their resonances in external acoustics

This paper briefly reviews a formulation that is based on the so-called conjugated infinite Astley-Leis elements to evaluate eigenvalues and eigenvectors in a state-space formulation. They are the solutions of a quadratic eigenvalue problem. We will present the computational example of an open cavity. For this, specified modes of the external and the internal problems are found and discussed. It is possible to identify most of the low-frequency normal modes of the corresponding closed cavity. Comparison between the eigenvalues of the closed and the open cavity provide an indication of the modal damping of these modes. Furthermore, the frequency independent eigenvectors or normal modes can be superimposed to reconstruct the harmonic solution. Resonances are found for most of the cavity modes. They are very differently damped.