The Extended Modal Reduction Method Applied to Rotor Dynamic Problems

In this paper, the existing Modal Reduction Method, which was developed to handle symmetric mass and stiffness matrices, is extended utilizing state-space formulation to handle nonsymmetric mass, damping, and stiffness matrices. These type of matrices typically accompany rotor dynamic problems since journal bearings supporting the rotor have nonsymmetric stiffness and damping characteristics. The purpose of modal reduction is to eliminate unimportant modes and degrees of freedom from the analytical model after they are found, so that further numerical analysis can be accelerated. The reduction described here leaves the retained eigenvalues and mode shapes unaltered from their original values. This method is demonstrated for a simple rotor problem having nonsymmetric system matrices including gyroscopic effects.