A Minimization Method for the Solution of the Eigenproblem Arising in Structural Dynamics
Abstract
This paper presents an iterative method to obtain a partial or complete solution of the general eigenproblem which does not require any preliminary modification to put it into the form of a special eigenvalue problem. The Rayleigh Quotient is minimized by the use of the conjugate gradient method to obtain the lowest eigenvalue and the associated eigenvector. The approach is extended to permit the intermediate eigenvalues and eigenvectors to be obtained by adapting a projection scheme which is akin to Rosen's Gradient Projection Method. This technique constrains the minimization search to the subspace M-orthogonal to the previously determined eigenvectors. A theoretical justification is presented that the quadratic convergence of the conjugate gradient method is preserved. The important computer storage advantages of the conjugate gradient method are extended by eliminating the need for assembled stiffness and mass matrices. A number of structural examples are presented to demonstrate the effectiveness, generality and stability of the method.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1968
- Accession Number
- ADA447804
Entities
People
- M. P. Kapoor
- R. L. Fox
Organizations
- Case Western Reserve University