The eigenvalue problem for damped gyroscopic systems

Abstract

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 real 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 systems in a decoupled way. Compared to the conventional complex mode decoupling method, this method virtually uses only real number computation, remains valid when the corresponding eigenvalue problem is defective and does not require solution of the left eigenvector problem. The structure of the decoupled dynamic equation is very satisfying, because it enhances understanding of the combination of damping with gyroscopic effects. For undamped gyroscopic systems, the decoupling method proposed degenerates to that of Meirovitch.