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Structural Engineering and Mechanics Volume 10, Number 5, November 2000 , pages 427-440 DOI: https://doi.org/10.12989/sem.2000.10.5.427 |
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Derivation of formulas for perturbation analysis with modes of close eigenvalues |
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Liu XL
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| Abstract | ||
| The formulas for the perturbation analysis with modes of close eigenvalues are derived in this paper. Emphasis is made on the consistency of the straightforward perturbation process, given the complete terms of perturbations in the zeroth-order, which is a form of Rayleigh quotient, and in the higher-orders. By dividing the perturbation of eigenvector into two parts, the first-order perturbation with respect to the modes of close eigenvalues is moved into the zeroth-order perturbation. The normality condition is employed to compute the higher-order perturbations of eigenvector. The algorithm can be condensed to a single mode with a distinct eigenvalue, and this can accelerate the convergence of the perturbation analysis. The example confirms that the perturbation approximation obtained from the suggested procedure is in a good accuracy on the eigenvalues, eigenvectors, and normality. | ||
| Key Words | ||
| eigenvalue problem, close eigenvalues, perturbation analysis | ||
| Address | ||
| Laboratorio Nacional de Engenharia Civil, Avenida do Brasil, 101, 1700-066 Lisboa Codex, Portugal | ||