Abstract
In this paper, a new solution method for the modified eigenvalue problem with specific application to structural dynamic reanalysis is presented. The method, which is based on the block Lanczos algorithm, is developed for multiple low rank modifications to a system and calculates a few selected eigenpairs. Given the solution to the original system Ax = λx, procedures are developed for the modified standard eigenvalue Problem (A + ΔA)x = λx, where 1ΔA = ΣjBSjBT, where Sj = S ∈ ℛp × p, p ≪ n and B ∈ ℛn × p is constant for all the perturbations Sj. 2ΔA = ΣiΣjBiSjBiT, where Bi ∈ ℛn × p may vary with the pertubations Sj. The procedures are then extended for the reciprocal and generalized eigenvalue problems so that they are directly applicable to the structural dynamic reanalysis problem. Numerical examples are given to demonstrate the applications of the method.
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