Abstract: Based on the free boundary theory and the variational method,a fast and accurate model for the calculation of the fluid-film forces under the Renolds boundary condition is presented.The model has been applied to the nonlinear dynamic behavior analysis of an imbalanced rigid rotor with two three-lobe bearing supports.Numerical simulation shows that the imbalanced rotor undergoes a bifurcation from synchronous motion to double period motion and at last loses its stability as chaotic motion. This paper also studied the influences of the rotor mass and the mass eccentricity. It is found that the threshold speed at which the rotor will lose stability decreases with the increase of rotor mass.The eccentricity influences the motion of the rotor seriously.The rotor threshold speed increases rapidly with the increase of mass eccentricity.Study of the elliptical bearing shows that the threshold speed of rotor supported by three-lobe bearings is higher than that of the elliptical bearings.