Development of Non-dimensional Dynamic Influence Function Method Based on Three-domain Decomposition Approach for Eigenvalue Extraction over Entire Frequency Range of Concave Membranes: Part 1(Theoretical Formulation and Verification)

This study developed a novel eigenvalue extraction method for geometrically complex concave membranes using the non-dimensional dynamic influence function (NDIF) method based on a three-domain decomposition approach. Contrary to conventional NDIF formulations, which suffer from numerical instability and failure to extract lower-order eigenvalues as the number of boundary nodes increases, the proposed method introduces an improved system matrix formulation that eliminates the need for matrix inversion at the local level. This enhancement fundamentally resolves the low-frequency divergence issue inherent in previous formulations. The validity and numerical accuracy of the proposed method were verified through a comparative analysis with exact solutions and FEM results for a rectangular membrane divided into three domains. The results confirmed that the proposed method can accurately extract eigenvalues across the entire frequency range, including the lower-order modes, regardless of boundary node density. This study focused on the theoretical formulation and validation using a relatively simple membrane model; application to more complex geometries will be presented in Part 2.