A flexible rotor bearing system is represented in detail utilizing the state of the art finite element technique. The mathematical model takes into account the gyroscopic moments, rotary inertia, shear deformation, internal viscous damping, hysteretic damping, linear as well as nonlinear stiffness, and damping for the finite bearing and the bearing support flexibility. Using a simple Timoshenko element and recognizing an analogy between the motion planes, a procedure is given that requires a construction of only three symmetric 4×4 matrices. As an application, the different effects of the bearing lining flexibility and the bearing support flexibility on the rotor stability behavior is studied and discussed. The necessary relation for general modal analysis is simply restated and integrated into the conventional spectral approach, thus developing a simple procedure for the calculation of the stochastic response of a general rotor dynamic system. An application to a light rotor bearing featuring a general spatial support and subjected to random disturbances is illustrated.

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