Improved non-dimensional dynamic influence function method based on tow-domain method for vibration analysis of membranes

Abstract

This article introduces an improved non-dimensional dynamic influence function method using a sub-domain method for efficiently extracting the eigenvalues and mode shapes of concave membranes with arbitrary shapes. The non-dimensional dynamic influence function method (non-dimensional dynamic influence function method), which was developed by the authors in 1999, gives highly accurate eigenvalues for membranes, plates, and acoustic cavities, compared with the finite element method. However, it needs the inefficient procedure of calculating the singularity of a system matrix in the frequency range of interest for extracting eigenvalues and mode shapes. To overcome the inefficient procedure, this article proposes a practical approach to make the system matrix equation of the concave membrane of interest into a form of algebraic eigenvalue problem. It is shown by several case studies that the proposed method has a good convergence characteristics and yields very accurate eigenvalues, compared with an exact method and finite element method (ANSYS).