The modern engineering industries rely heavily on the reliable operation of rotating machinery, e.g., steam turbine and gas turbine. These rotating machineries are inevitable to be excited by the unbalance mass forces, the oil film forces and seal forces. Moreover, the turbines installed in an aircraft as well as vessel are also excited by the base vibration. In order to retain the healthy operation and prolong the interval between overhauls, an enormous amount of experimental and theoretical investigations have been focused on the dynamic behaviors of the rotor system. The dynamic characteristics of the rotor system influenced by the single source of vibration, such as unbalance, flowing lubricating oil, sealing medium etc., and combined sources of vibration have also been thoroughly researched. However, the dynamic responses of the rotor-bearing-foundation system subjected to labyrinth seal forces have seldom been studied. Furthermore, the previous analyses of the rotor dynamics mostly were linear. In fact, the fluid film forces are strongly nonlinear functions of the displacement and velocity of the rotor. As a result, the rotordynamics of the turbine is highly nonlinear. It is not accurate enough to be considered from a linear point of view. Applying the energy method, this paper established a dynamic model of the rotor-bearing-foundation-labyrinth seal system. The influences of the geometrical parameters and operating conditions, such as mass eccentricities, inlet pressure and rotational speed etc., on the nonlinear dynamic behaviors of the rotor system are numerically studied. The responses of the same system excited by one side of and both sides of base movement are also comparatively analyzed by means of spectrum cascades, bifurcation diagrams and whirl orbits as well as Poincaré maps.

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