Eigensensitivity analysis of damped systems with distinct and repeated eigenvalues. (English) Zbl 1302.65247
Summary: This paper considers the computation of eigensolution sensitivity of viscously damped eigensystems with distinct and repeated eigenvalues. To simplify the computation, a combined normalization, which combines two traditional normalizations, is presented. Based on the combined normalization, a method for sensitivity analysis of eigenvalues and eigenvectors is studied. In the case of distinct eigenvalues, the proposed method can determine the eigenvector derivatives directly and is robust since the components of coefficient matrices are all of the same order of magnitude. The computational cost of the second-order sensitivities of eigenvectors can be reduced remarkably since the matrix decomposition of the coefficient matrix is available from the computation process of the first-order eigensensitivities. In the case of repeated eigenvalues, an algorithm is presented for computing the eigensolution sensitivities. The algorithm maintains \(N\)-space without using state-space equations such that the computational cost is reduced. The method is accurate, compact, numerically stable and easy to be implemented. Finally, three numerical examples have demonstrated the validity of the proposed method. The capacity of predicting the changes of eigensolutions with respect to the changes of design parameters in terms of the first- and second-order eigensensitivities is studied with application to the analysis of a two-stage floating raft isolation system.
MSC:
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
Keywords:
design sensitivity analysis; eigensensitivity; damped systems; repeated eigenvalues; floating raftSoftware:
mctoolboxReferences:
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