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In this paper the dynamic behavior of a rotating system which includes rotor (shaft), ball bearing and disk in stationary condition and different speeds is investigated. There are nonlinear characteristics in these systems which cause the linear modeling is not sufficiently accurate. So, in this paper the nonlinear dynamic equations of the system are derived and solved. To derive the equations of the system, Hamiltonian method is used, and complex coordinate transform is used to reduce the number of equations. After solving the equations, to investigate the vibrational properties of the system, time response diagram, dynamic orbit, frequency response, and mode shape of the rotor is plotted. To validate the analytical results, finite element method by ANSYS (workbench) software is used.There is a good conformity betweenthe analytical results and finite element results in resonance frequencies of the system in the first three modes which indicates the sufficient accuracy in nonlinear modeling. It can be concluded from nonlinear modeling that the decay rate is negative for the all modes which is indicates the stability of the all modes. Also, the maximum vibration amplitude in the bearing and rotor occurs in third and second modes respectively. Unbalance phase difference of 90 degrees in two discs causes the excitation of all three frequency modes, whereas by unbalance phase difference of 0 or 180 degrees in two discs,only the odd modes (first and third) and the even modes (second) is excited respectively.

Keywords: Vibration of rotating systems, nonlinear modeling, Finite element, unbalance phase difference

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