Technique of checking missed eigenvalues for eigenproblem with damping matrix

In the case of the non-proportionally damped system such as the soil-struct ure interaction system, the structural control system and composite structu res, the eigenproblem with the damping matrix should be necessarily perform ed to obtain the exact dynamic response. However, most of the eigenvalue an alysis methods such as the subspace iteration method and the Lanczos method may miss some eigenvalues in the required ones. Therefore, the eigenvalue analysis method must include a technique to check the missed eigenvalues to become the practical tools. In the case of the undamped or proportionally damped system the missed eigenvalues can easily be checked by using the wel l-known Sturm sequence property, while in the case of the nonproportionally damped system a checking technique has not been developed yet. In this pap er, a technique of checking the missed eigenvalues for the eigenproblem wit h the damping matrix is proposed by applying the argument principle, To ver ify the effectiveness of the proposed method, two numerical examples are co nsidered. Copyright (C) 2001 John Wiley & Sons, Ltd.