Robust non-dimensional dynamic influence function method using rank-aware determinant evaluation for eigenmode analysis of acoustic cavities

A rank-aware determinant evaluation scheme is presented to improve the non-dimensional dynamic influence function (NDIF) method for accurate eigenvalue and eigenmode analyses of arbitrarily shaped two-dimensional acoustic cavities. In the conventional NDIF method, lower-order eigenvalues in the low-frequency range may be missed when the number of boundary nodes is increased to enhance higher-order accuracy. This study first shows that this limitation originates from ill-conditioning and rank deficiency of the system matrix in the low-frequency region, which makes direct determinant evaluation unreliable. To address this issue, a practical determinant-evaluation scheme is developed by incorporating the rank information of the acoustic-cavity system matrix together with that of the corresponding membrane system matrix. In addition, a discontinuity-removal procedure is introduced to eliminate stepwise discontinuities in the determinant curve caused by discontinuous rank variations, thereby enabling robust identification of eigenvalues. The proposed method is validated using three example studies: a circular cavity with an exact solution and two arbitrarily shaped cavities. The extracted eigenvalues and mode shapes show exact agreement with the analytical solutions for the circular cavity and close agreement with finite-element method results for the arbitrarily shaped cavities.