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A Lanczos‐based method for structural dynamic reanalysis problems
Author(s) -
Carey Cheryl M. M.,
Golub Gene H.,
Law Kincho H.
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620371610
Subject(s) - lanczos resampling , eigenvalues and eigenvectors , mathematics , reciprocal , block (permutation group theory) , rank (graph theory) , lanczos algorithm , constant (computer programming) , algorithm , combinatorics , computer science , physics , philosophy , linguistics , quantum mechanics , programming language
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 = λ x , procedures are developed for the modified standard eigenvalue Problem ( A + Δ A )x̄ = λ x̄, where 1 Δ A = Σ j BS j B T , where S j = S j T∈ ℛ p × p , p ≪ n and B ∈ ℛ n × p is constant for all the perturbations S j . 2 Δ A = Σ i Σ j B i S j B i T , where B i ∈ ℛ n × p may vary with the pertubations S j .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.