From the viewpoint of nonlinear dynamics, the stability and bifurcation of the rotor dynamical system supported in gas bearings are investigated. First, the dynamical model of gas bearing-Jeffcott rotor system is given, and the finite element method is used to approach the unsteady Reynolds equation in order to obtain gas film forces. Then, the method for stability analysis of the unbalance response of the rotor system is developed in combination with the Newmark-based direct integral method and Floquet theory. Finally, a numerical example is presented, and the complex behaviors of the nonlinear dynamical system are simulated numerically, including the trajectory of the journal and phase portrait. In particular, the stabilities of the system’s equilibrium position and unbalance responses are studied via the orbit diagram, phase space, Poincaré mapping, bifurcation diagram, and power spectrum. The results show that the numerical method for solving the unsteady Reynolds equation is efficient, and there exist a rich variety of nonlinear phenomena in the system. The half-speed whirl encountered in practice is the result from Hopf bifurcation of equilibrium, and the numerical method presented is available for the stability and bifurcation analysis of the complicated gas film-rotor dynamic system.

Aerodynamic Analysis of a Localized Flexible Airfoil at Low Reynolds Numbers - Volume 11 Issue 4 - Wei Kang, Jia-Zhong Zhang, Pei-Hua Feng

In order to accurately study the effect of curvature on panel aeroelastic behaviors, a fluid–structure coupling algorithm is adopted to analyze the curved panel flutter in transonic and supersonic airflows. First, the governing equation for the motion of the curved panel and the structure solver are presented. Then, the fluid governing equations, the fluid solver, and the fluid–structure coupling algorithm are introduced briefly. Finally, rich aeroelastic responses of the curved panel are captured using this algorithm. And the mechanisms of them are explored by various analysis tools. It is found that the curvature produces initial aerodynamic loads above the panel. Thus, the static aeroelastic deformation exists for the curved panel in stable state. At Mach 2, with its stability lost on this static aeroelastic deformation, the curved panel shows asymmetric flutter. At Mach 0.8 and 0.9, the curved panel exhibits only positive static aeroelastic deformation due to this initial aerodynamic load. At Mach 1.0, as the dynamic pressure increases, the curved panel loses its static and dynamic stability in succession, and behaves as static aeroelastic deformations, divergences, and flutter consequentially. At Mach 1.2, with its stability lost, the curved panel flutters more violently toward the negative direction. The results obtained could guide the panel design and panel flutter suppression for flight vehicles with high performances.

Unsteady Flow Separation and High Performance of Airfoil with Local Flexible Structure at Low Reynolds Number - Volume 16 Issue 3 - Peng-Fei Lei, Jia-Zhong Zhang, Wei Kang, Sheng Ren, Le Wang