An efficient algebraic method for computing eigensolution sensitivity of asymmetric damped systems

In this paper, an efficient algebraic method for the computation of eigensolution derivatives of asymmetric damped systems with distinct eigenvalues is presented. By introducing an additional and new normalization condition, we construct two extended systems of linear equations with nonsingular coefficient matrices which are transpose to each other. We can compute the derivatives of the eigenvalues and their associated right and left eigenvectors by solving the two systems, respectively. In this way, the CPU computation time and the storage space are considerably reduced. Finally, a numerical example is included to demonstrate the validity of the proposed method.