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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.

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Oil journal bearings are one of the most common parts of high load carrying rotating machine. Stability of these bearings can be affected by various stimulus such as changes in loading and lubrication conditions. Therefore, identification of the dynamic response of journal bearings can improve the control and fault detection process of rotor-bearings systems and prevent them from placing in critical operation condition. Since past, the mass unbalance of rotor is proposed as an effective factor on the dynamic behavior and long life of bearings. For this reason, in this research the effects of this parameter on the stability of hydrodynamic two lobe noncircular journal bearing with micropolar lubricant is investigated based on the nonlinear dynamic model. To achieve this goal, the governing Reynolds equation is modified with respect to micropolar fluid theory and the equations of rotor motion are derived considering the mass unbalance parameter. The static and dynamic pressure distributions of the lubricant film and the components of displacement, velocity and acceleration of the rotor are obtained by simultaneous solution of the Reynolds equation and the equations of rotor motion. Investigation of results in terms of dynamic trajectory, power spectrum, bifurcation diagram and Poincare map show that the dynamic behavior of two lobe bearings appears in different manner with variation of mass unbalance of rotor. The response of analyzed dynamic system include converge oscillations to the equilibrium point, periodic, KT periodic and quasi periodic behavior and also divergent disturbances which leads to collision between the rotor and bearing.

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Dynamics analysis of the rotational axially moving pipe conveying fluid under simply supported condition investigated in this research. The pipe assumed as Euler Bernoulli beam. The gyroscopic force and mass eccentricity were considered in the research. Equations of motion are derived using Hamilton’s principle, resulting in two partial differential equations for the transverse motions. The non-dimensional equations were discretized via Galerkin’ method and were solved using Rung Kutta method (order 15s). The frequency response curve obtained in terms of non-dimensional rotational speed. The bifurcation diagrams are represented in the case that the non-dimensional fluid speed, non-dimensional axial speed and non-dimensional rotational speed were respectively varied and the dynamical behavior is numerically identified based on the Poincare' portrait. Numerical simulations indicated that the system response increases by increasing non-dimensional axial speed of the pipe, non-dimensional fluid speed and non-dimensional rotational speed of the pipe and then decreases after passing critical area. The system is unstable at critical point associated with non-dimensional axial speed. Poincare portrait indicates periodic motion in transverse vibrations of the pipe at some points of control parameters. Phase portrait and FFT (Fast Fourier Transform) diagrams were used for validation of the results.