In this article, using finite element method the effects of the preload on the nonlinear dynamic behavior of the noncircular two lobe aerodynamic journal bearing have been investigated. Assuming that the rotor is solid, the governing Rynolds equations for both the gas lubricant and rotor equation of motion in static and dynamic conditions have been derived and performance of the noncircular aerodynamic journal bearing in different conditions has been evaluated. Rung Kutta method has been used to solve the time dependent equations of motions of noncircular aerodynamic journal bearing and its gas lubricant. Using the numerical results, to investigate the motion of the center of the rotor in dynamic conditions, the graphs of frequency response, power spectrum, dynamic trajectory, Poincare map and bifurcation diagram have been plotted. The results show periodic, quasi periodic and chaotic rotor behavior for different bearing preload. It is concluded that appropriate selection of rotor parameters like its preload and suitable design and fabrication of rotor and its bearing can prevent any undesirable perturbed motions of the shaft and both the collision and wear of the rotor and bearing.