Eigensensitivity computation of asymmetric damped systems using an algebraic approach

An algebraic method is presented for simultaneous computation of the derivatives of eigenvalues and those of their associated right and left eigenvectors, for asymmetric damped systems. The proposed method requires only the knowledge of the eigensolution to be differentiated and can be used to compute first-, second- and higher-order derivatives of the eigenvalues and their associated eigenvectors. To demonstrate the efficiency of the proposed method, a finite-element asymmetric damped rotor model is considered as a numerical example. The rotor shaft diameter has been chosen as a design parameter. Comparison of first- and second-order eigensensitivity results computed by the proposed approach to those computed by other approaches shows clearly the efficiency of the proposed method.