Solution Techniques for Large Eigenvalue Problems in Structural Dynamics.
Abstract
This study treats the determination of eigenvalues and eigenvectors of large algebraic systems. The methods developed are applicable to finding the natural frequencies and modes of vibration of large structural systems. For distinct eigenvalues the method is an application of the modified Newton-Raphson method that turns out to be more efficient than the standard competing schemes. For close or multiple eigenvalues, the modified Newton-Raphson method is generalized to form a new process. The entire set of close eigenvalues and their eigenvectors are found at the same time in a two-step procedure. The subspace of the approximate eigenvectors is first projected onto the subspace of the the true eigenvectors. If the eigenvalues are multiple, the results of the first stage indicate this fact and the process terminates. If they are merely close, a single rotation in the newly found space solves a small eigenvalue problem and provides the final results for the close set. The procedure for subspace projection can be expressed as a simple extremum problem that generalizes the known extremum property of eigenvectors. Computational effort and convergence are studied in three example problems. The method turns out to be more efficient than subspace iteration. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1979
- Accession Number
- ADA098786
Entities
People
- Arthur R. Robinson
- In-won Lee
Organizations
- University of Illinois Urbana–Champaign