Lanczosbased method for structural dynamic reanalysis problems
Abstract
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 = lambda x, procedures are developed for the modified standard eigenvalue problem (A + Delta A)xbar = lambdabar xbar, where (1) Delta A = Sigma(sub j)BS(sub j)B(sup T), where S(sub j) = S(sub j)(sup T)epsilon R(sup p x p), p very much less than T n and B epsilon R(sup n x p) is constant for all the perturbations S(sub j), (2) Delta A = Sigma(sub i)Sigma(sub j)B(sub i)S(sub j)B(sub i)(sup T), where B(sub i) epsilon R(sup n x p) may vary with the perturbations S(sub 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.
 Publication:

International Journal for Numerical Methods in Engineering
 Pub Date:
 August 1994
 DOI:
 10.1002/nme.1620371610
 Bibcode:
 1994IJNME..37.2857C
 Keywords:

 Dynamic Response;
 Dynamic Structural Analysis;
 Eigenvalues;
 Mathematical Models;
 Matrix Theory;
 Algorithms;
 Computer Techniques;
 Eigenvectors;
 Perturbation;
 Structural Mechanics