A PRACTICAL ALGORITHM FOR THE EFFICIENT COMPUTATION OF EIGENVECTOR SENSITIVITIES

Derivatives of eigenvalues and eigenvectors have become increasingly i mportant in the development of modern numerical methods for areas such as structural design optimization, dynamic system identification and dynamic control, and the development of effective and efficient method s for the calculation of such derivatives has remained to be an active research area for several decades. In this paper, a practical algorit hm has been developed for efficiently computing eigenvector derivative s of generalized symmetric eigenvalue problems. For eigenvector deriva tive of a separate mode, the computation only requires the knowledge o f eigenvalue and eigenvector of the mode itself and an inverse of syst em matrix accounts for most computation cost involved. In the case of two close modes, the modal information of both modes is required and t he eigenvector derivatives can be accurately determined simultaneously at minor additional computational cost. Further, the proposed method has been extended to the case of practical structural design where str uctural modifications are made locally and the eigenderivatives of the modes concerned before are still of interest. By combining the propos ed algorithm together with the proposed inverse iteration technique an d singular value decomposition theory, eigenproperties and their deriv atives can be very efficiently computed. Numerical results from a prac tical finite element model have demonstrated the practicality of the p roposed method. The proposed method can be easily incorporated into co mmercial finite element packages to improve the computational efficien cy of eigenderivatives needed for practical applications.