The Derivatives of Repeated Eigenvalues and their Associated Eigenvectors
MI Friswell (University of Wales Swansea)
Journal of Vibration and Acoustics, Vol. 118, No. 3, July 1996, pp. 390-397
This paper considers the calculation of eigenvalue and eigenvector derivatives when the eigenvalues are repeated. An extension to Nelson's method is used to calculate the first order derivatives of eigenvectors when the derivatives of the associated eigenvalues are also equal. The continuity of the eigenvalues and eigenvectors is discussed, and the discontinuities in the eigenvectors, when they are regarded as functions of two or more design parameters, is demonstrated. The validity of Taylor series for the eigenvalues and eigenvectors is examined and the use of these series critically assessed.
This material has been published in the Journal of Vibration and Acoustics, Vol. 118, No. 3, July 1996, pp. 390-397, the only definitive repository of the content that has been certified and accepted after peer review. The copyright has been assigned to the American Society of Mechanical Engineers.
Link to paper using doi: 10.1115/1.2888195
Journal of Vibration and Acoustics