A quasi-frontal subspace iteration method for finite element dynamic analysis and its application

Combining with linear algebra, an effective method, in which the idea of the frontal method is applied to the subspace iteration approach, is presented in this paper for calculating natural frequencies and the corresponding mode shapes of large structural systems. It has an advantage over the bandform subspace iteration method in that the present method does not require generation and storage of stiffness and mass matrices for the whole structure. Thus, the method requires minimum computer storage, and for large-scale finite element dynamic analysis, it is possible to carry out the proposed algorithm 3sing a personal computer. The results show that the storage required in the present method is at least less than one-third that required in the bandform subspace iteration method. Based on the present method, the first twelve natural frequencies and the corresponding mode shapes of a complex gear with different structure sizes and web arrangements have been calculated on a PC. The calculated results agree well with the experimental results and several important conclusions are also obtained for designing gears.