A Combination of the Lanczos Algorithm with the Substructure Technique

Abstract

A modified Lanczos method combined with a substructure technique was used for calculating natural frequencies and mode shapes of large structural systems. The method does not require generation and storage of stiffness and mass matrices of the original structure. It uses only the stiffness and mass matrices of each substructure. No approximating assumptions are needed other than the usual assumption of a linear elastic system modelled by finite elements. Thus, natural frequencies and the mode shapes for the finite element model employed are the same as those with or without the substructuring algorithm. The method is demonstrated by calculating the first ten natural frequencies and the corresponding mode shapes for an open truss helicopter tail-boom structure. (C) 1995 Academic Press Limited