Development of the NDIF Method based on the Sub-domain Method Overcoming the Non-extraction Problem of Low-order Eigenvalues for Concave Membranes: Part 1(Theoretical Formulation and Verification)

The NDIF method, developed by the author, exhibits a significant limitation in that low-order eigenvalues cannot be accurately obtained as the number of nodes increases. Recent studies on membranes, acoustic cavities, and plates have introduced an ‘improved NDIF method’ that addresses this issue; however, further research is required to determine whether this method is applicable to concavely shaped membranes, which necessitate the use of the sub-domain method to divide the concave domain into several convex domains. In this paper, it is demonstrated that the aforementioned ‘improved NDIF method’ is not valid for concave membranes. A new NDIF method, specifically designed to be effective for concave membranes, is proposed. This new method was developed by first identifying the reasons for the invalidity of the improved NDIF method and then reconstructing the system matrix without reduction. To verify the accuracy and validity of the proposed method, example studies were conducted on a rectangular membrane with exact solutions and an arbitrarily shaped membrane featuring a deep groove.