Eigenvalue and eigenvector derivatives are often needed in structural dynamic analyses such as structural optimisation, structural modification prediction and system identification. This paper examines the various different methods developed for calculating derivatives of eigenvalues and eigenvectors with emphasis on their advantages and disadvantages in terms of computational cost and numerical accuracy. The methods are extended to the case where structural damping is involved and the eigenvalues and eigenvectors become complex. Possible applications of different methods in structural dynamics are highlighted and guidelines are given for dynamic analyst to choose which method is the most appropriate for their specific applications.
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