Safeguarded use of the implicit restarted lanczos technique for solving non‐linear structural eigensystems
Mohammedi R. Abdel‐Aziz · International Journal for Numerical Methods in Engineering · 1994
Abstract This paper presents a new algorithm for evaluating the eigenvalues and their corresponding eigenvectors for large‐scale non‐linear eigensystems in structural dynamics. The algorithm is based on solving a sequence of algebraic eigenproblems and updating the parameter λ. The implicitly restarted Lanczos method had been determined to be well suited for solving the linear eigenproblems that arise in this context. A zero‐finder approach that uses rational interpolation to approximate the generalized eigenvalues has been developed to update λ. The methodology of the new algorithm developed here is designed to evaluate a subset of the parametrized non‐linear eigencurves at specific values of λ. Numerical experiments show that the new eigensolution technique is superior to existing approaches for large‐scale problems and competitive for small‐size problems. The main emphasis of this contribution is the derivation and analysis of this scheme for non‐linear structural eigensystems.