A continuous modeling of nonlinear rotor-bearing systems is presented in this paper. The shaft is treated as a distributed parameter system using Timoshenko beam theory. A close form, steady-state response of the system is solved analytically for the first time. For cubic nonlinear bearings, the response is composed of three components, synchronous vibration, subsynchronous, and supersynchronous vibration. The harmonic balance method is used to calculate the nonlinear bearing forces. Two examples of nonlinear rotor-bearing systems are shown to illustrate the analysis procedure and the nonlinear characteristics of the system. Solutions from simplified systems are also derived for comparison.

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