This paper studies the bifurcation of a rigid rotor supported by a gas film bearing. A time-dependent mathematical model for gas journal bearings is presented. The finite differences method and the Successive Over Relation (S.O.R) method are employed to solve the Reynolds’ equation. The system state trajectory, Poincare´ maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor center in the horizontal and vertical directions under different operating conditions. The analysis shows how the existence of a complex dynamic behavior comprising periodic and subharmonic response of the rotor center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems.

No abstract

The new double side approach method combining the mathematical programming and the subdomain method in the method of weighted residual is presented in this article. Under the validation of maximum principle, and up on the subdomain method, the differential equation can be transferred into a bilateral inequality problem. Applying the genetic algorithms helps to find optimal solutions of upper and lower bounds which satisfy the inequalities. Here, the method is first verified by analyzing the deflection of elliptical clamped plate problem under various aspect ratios and further apply it to analyze the clamped super-elliptical plates problem. By using this method, the good approximate solution can be obtained accurately.

No abstract

No abstract