Rapid reanalysis of the generalized eigenvalue problem of locally modified linear dynamical systems

A computationally efficient method for the reanalysis of the damped generalized eigenvalue problems associated with linear dynamical systems with local damping and stiffness modifications is developed. No restrictions are imposed on the damping of the system and the modifications in the damping and the stiffness can be independent of each other. The application of the developed method to the undamped generalized eigenvalue problem with mass and stiffness modifications is also discussed. The proposed method achieves up to three orders of magnitude gains in computational efficiency compared to the conventional solution procedures.