Advanced non-dimensional dynamic influence function method considering the singularity of the system matrix for accurate eigenvalue analysis of membranes

Abstract

An advanced non-dimensional dynamic influence function method (NDIF method) for highly accurate free vibration analysis of membranes with arbitrary shapes is proposed in this paper. The existing NDIF method has the weakness of not offering eigenvalues and eigenmodes in the low frequency range when the number of boundary nodes of an analyzed membrane is increased to obtain more accurate result. This paper reveals that the system matrix of the membrane becomes singular in the lower frequency range when the number of the nodes increases excessively. Based on this fact, it provides an efficient way to successfully overcome the weaknesses of the existing NDIF method and still maintain its accuracy. Finally, verification examples show the validity and accuracy of the advanced NDIF method proposed.