THE EIGENVALUE PROBLEM FOR DAMPED GYROSCOPIC SYSTEMS

This paper develops the dynamic orthogonal decoupling method in order to decouple damped gyroscopic structural dynamic systems. The Arnoldi method is extended to solve the generalised eigenvalue problem via a r eal Schur decomposition. Very interesting results are obtained, which show that this method cannot only obtain the eigenvalues of the system , but can also solve dynamic response of damped gyroscopic dynamic sys tems in a decoupled way. Compared to the conventional complex mode dec oupling method, this method virtually uses only real number computatio n, remains valid when the corresponding eigenvalue problem is defectiv e and does not require solution of the left eigenvector problem. The s tructure of the decoupled dynamic equation is very satisfying, because it enhances understanding of the combination of damping with gyroscop ic effects. For undamped gyroscopic systems, the decoupling method pro posed degenerates to that of Meirovitch. Copyright (C) 1997 Elsevier S cience Ltd.