论文信息 - Sensitivity of Repeated Eigenvalues to Perturbations

Sensitivity of Repeated Eigenvalues to Perturbations

Two methods for calculating the derivatives of a repeated eigenvalue of viscously damped vibrating systems with respect to a parameter are given. The first method implements the subspace spanned by the eigenvectors corresponding to the repeated eigenvalue. The second method is based on an explicit formula that uses the characteristic equation directly, without explicitly employing the eigenvector data. Examples demonstrate the various results.

Yitshak M. Ram | Su-Seng Pang | Kanika N. Vessel

[1] Sylvan Elhay,et al. An affine inverse eigenvalue problem , 2002 .

[2] C. R. Crawford. A Stable Generalized Eigenvalue Problem , 1976 .

[3] Yitsak M. Ram,et al. Eigenproblem error bounds with application to symmetric dynamic system modification , 1990 .

[4] Richard B. Nelson,et al. Simplified calculation of eigenvector derivatives , 1976 .

[5] I. U. Ojalvo,et al. Efficient computation of modal sensitivities for systems with repeated frequencies , 1988 .

[6] W. Kahan,et al. The Rotation of Eigenvectors by a Perturbation. III , 1970 .

[7] B. Parlett. The Symmetric Eigenvalue Problem , 1981 .

[8] Uwe Prells,et al. Calculating Derivatives of Repeated and Nonrepeated Eigenvalues Without Explicit Use of Eigenvectors , 2000 .

[9] R. Fox,et al. Rates of change of eigenvalues and eigenvectors. , 1968 .

[10] Uwe Prells,et al. Partial Derivatives of Repeated Eigenvalues and Their Eigenvectors , 1997 .

[11] Ting-Yu Chen,et al. Design sensitivity analysis for repeated eigenvalues in structural design , 1993 .

[12] K. T. Joseph. Inverse eigenvalue problem in structural design , 1992 .

[13] Yitshak M. Ram,et al. Eigenvector Error Bounds and Their Applications to Structural Modification , 1993 .