Large Limit Cycle Oscillations Research Articles

Non-linear Dynamic Characteristics of High-Speed Wheel-Rail Interface Considering Surface Topography and Liquid Medium

In this work, the force-deflection characteristics, and the nonlinear vibration of the wheel-rail interaction with surface roughness and liquid medium are studied. The statistical micro-contact Greenwood and Williamson model is used to characterize the rough surface. The load sharing theory is used to determine the analytical elastic contact force-deflection and damping force-deflection relationships, which are further approximated by power law functions. The nonlinear contact stiffness and damping characteristics are illustrated for different rough surface topographies and running speeds. The natural frequency is solved by assuming small covariates and defining time variables of different scales. Effects of surface topography and liquid medium on the natural frequency of the wheel-rail interface system are studied. The first-order harmonic responses under harmonic excitation are further determined as well as the jump-up and jump-down responses for different rough surface topographies, excitation loads, liquid mediums and running speeds. It is shown that the resonance region and the peak value of the vibration amplitude increase as the surface roughness, running speed and excitation load increase; whilst the jump-up and jump-down frequencies decrease. In addition, the system can change from a monostable to a bistable structure when surface roughness and excitation force increase and large limit cycle oscillation can occur.

Experimental study on the flutter-induced motion of two-degree-of-freedom plates

This work investigates the flow-induced motion originating from the classical-flutter instability, and it is motivated by energy-harvesting applications. The influence of several sets of dynamic parameters is studied, improving the scientific understanding of the large-amplitude response and guiding the design of more unstable configurations. Wind-tunnel tests were conducted on elastically-suspended rigid models with an elongated rectangular cross section, undergoing a two-degree-of-freedom motion with transverse (heaving) and rotational (pitching) components. The aeroelastic setup was specifically developed to allow for a large-amplitude motion (about one chord in heaving and more than 90°in pitching) and to simulate an energy-conversion apparatus by increasing the heaving damping (up to about 18% of the critical one) through eddy-current dampers. After a sub-critical bifurcation, large limit-cycle oscillations were recorded, with steady-state amplitudes increasing with the flow speed. For some configurations, a low-amplitude response was also observed around the instability threshold. It was found that a small mass unbalance aft of the elastic axis significantly fosters the system instability and affects the heaving and pitching motion amplitudes. The latter are also markedly influenced by the still-air frequency ratio. In the presence of high values of the heaving damping, the post-critical amplitude is usually reduced, although a destabilising effect of damping was observed in some specific cases. Finally, the motion is magnified for lower-inertia systems.

Bifurcation\instability forms of high speed railway vehicles

The China high speed railway vehicles of type CRH2 and type CRH3, modeled on Japanese high speed Electric Multiple Units (EMU) E2 series and Euro high speed EMU ICE3 series possess different stability behaviors due to the different matching relations between bogie parameters and wheel profiles. It is known from the field tests and roller rig tests that, the former has a higher critical speed while large limit cycle oscillation appears if instability occurs, and the latter has lower critical speed while small limit cycle appears if instability occurs. The dynamic model of the vehicle system including a semi-carbody and a bogie is established in this paper. The bifurcation diagrams of the two types of high speed vehicles are extensively studied. By using the method of normal form of Hopf bifurcation, it is found that the subcritical and supercritical bifurcations exist in the two types of vehicle systems. The influence of parameter variation on the exported function Rec 1(0) in Hopf normal form is studied and numerical shooting method is also used for mutual verification. Furthermore, the bifurcation situation, subcritical or supercritical, is also discussed. The study shows that the sign of Re(λ) determinates the stability of linear system, and the sign of Rec 1(0) determines the property of Hopf bifurcation with Rec 1(0)>0 for supercritical and Rec 1(0)<0 for subcritical.