Efficient Computation of Mode-Shape Derivatives for Large Dynamic Systems

This paper is concerned with the simplified numerical computation of eigenvector derivatives for very large problems with symmetric, banded matrices, such as those ordinarily encountered in structural dynamic systems. Starting with a brief review of existing alternate computation schemes, the paper focuses on Nelson's work, which is at present generally accepted as the most computationally efficient method. Two competitive and more traditional alternatives to Nelson's approach, one direct and one iterative, are offered. No claim is made that either of these methods are superior to Nelson's, but they do offer viable and more conventional alternatives. Also discussed is the common case of repeated, or closely spaced, eigenvalues, which was not treated by Nelson. A procedure for extending Nelson's ideas for such cases is proposed.