Full-frequency Eigenvalue Extraction of Membranes with an Internal Hole using an Improved Domain-decomposition-based NDIF Method: Part 1 (Theoretical Formulation and Verification)

In this study, a significant limitation of the conventional domain-decomposition-based nondimensional dynamic influence function (NDIF) method is addressed. The final system matrix is formulated to be constructed systematically, eliminating the inefficient requirement of re-deriving the entire matrix whenever the number of subdomains changes. This improved formulation is applied to a membrane with an internal hole to investigate whether the lower-order eigenvalue loss problem, which typically occurs as the number of boundary nodes increases, persists in such a configuration. A numerical example is considered to verify the effectiveness, stability, and accuracy of the proposed method. The numerical results demonstrate that the lower-order eigenvalue loss problem indeed occurs in membranes with an internal hole when using the conventional method. However, the improved NDIF method successfully resolves this problem, providing stable and accurate eigenvalue extraction over the entire frequency range regardless of the number of boundary nodes.