Eigenvalue Analysis of Thin Plate with Complicated Shapes By a Novel Infinite Element Method

Abstract

A novel infinite element method (IEM) is presented for solving plate vibration problems in this paper. In the proposed IEM, the substructure domain is partitioned into multiple layers of geometrically similar finite elements which use only the data of the boundary nodes. A convergence criterion based on the trace of the mass matrix is used to determine the number of layers in the IE model partitioning process. Furthermore, in implementing the Craig-Bampton (CB) reduction method, the inversion of the global stiffness matrix is calculated using only the stiffness matrix of the first element layer. The validity and performance of the proposed method are investigated by means of four illustrative problems. The first example considers the case of a simple clamped rectangular plate. It is observed that the IEM results are consistent with the theoretical results for first six natural frequencies. The second example considers the frequency response of a clamped rectangular plate with a crack. The main feature of IEM is that a very fine and good quality virtual mesh can be created around the crack tip. The third and fourth examples consider the natural frequency of a multiple point supported plate and a perforated plate, respectively. The results are obtained just need to adjust the reference point or boundary nodes. The parametric analyses for various geometric profiles are easy to be conducted using these numerical techniques. In general, the results presented in this study have shown that the proposed method provides a direct, convenient and accurate tool for eigenvalue analysis of thin plate structure with complicated shapes.