Abstract
A very effective method of stability analysis is developed for an anisotropic rotating shaft supported by some unsymmetrical bearings. The rotating shaft is modeled as a lumped mass system with large degrees of freedom. Then, the equation of motion of the system becomes parametrically excited linear system with large degrees of freedom. The stability analysis of this system is very difficult. In the presented method, the reduction model is constructed by using only a few dominant modes. The dominant modes are extracted from the complex eigenmodes derived from constant term of the equation of motion by using the approximate state transition matrix derived by the original model. The stability of the original model can be determined from the reduction model very efficiently and accurately. From the results of numerical computation, it is confirmed that the present method is very effective for the mechanical design but the analysis by using a model with small degrees of freedom is not accurate sufficiently.
