Bifurcation and responses analysis of two-dimension panel with external excitation in subsonic flow

Along with the development of high speed multiple unitetrain and intercity railroad, the high speed technology has become thedevelopment direction of train. With the increase of speed, the aerodynamicproblems of such train are emerging, while neglected in low speed. Futuretrains will increase their speeds substantially, and if so, aerodynamicforces may influence train running safety and affect passenger's comfort. Sothe aeroelasticity of high speed train is the problem to be urgently andpromptly solved. Because the high speed train adopts stream line design todecrease running resistance, lots of panel structures such as body skin arewidely used. When train runs with lower speed, these panel structures willvibrate with small amplitude and can not be inhibited at all. But undercombined aerodynamic forces and wheel-rail excitation, complicatedaeroelasticity phenomena of these panel structures may occur.The bifurcation and responses of two-dimension panel with externalexcitation in subsonic flow are studied in this paper. Based on thepotential theory of incompressible flow, the aerodynamic pressure for airacting on the top side of the panel is acquired. The wheel-rail excitationis simplified as external forcing acting on the panel. The cubic stiffnessand viscous damper in middle of the panel are considered. The nonlineargoverning motion equations are reduced to a series of ordinary differentialequations by the Galerkin method. The Runge-Kutta numerical method is usedto conduct numerical simulations. The distribution of non-single periodareas of the panel system are indicated in differential parameter planes.The effect of three dimensionless parameters, namely viscous dampingcoefficient \sigma , external forcing amplitude \beta and dynamicpressure increment \Delta \lambda , is emphatically investigated.The results of this paper show that the pitchfork bifurcation occurs withthe increase of dynamic pressure, and the number and stability of theequilibrium points change after the dynamic pressure exceeds the criticalvalue. In differential single period regions, the system motion trajectoriesin phase-plane portraits change rhythmically.1. In the parameter plane \sigma-\beta, the number of non-singleperiod regions decreases with the increase of \sigma ; the non-singleperiod regions and single period regions appear alternately with theincrease of \beta .2. In the parameter plane \Delta \lambda-\beta, the non-single periodregion number firstly increases and then decreases with the increase of\Delta \lambda ; the non-single period regions and single period regionsappear alternately with the increase of \beta .3. In the parameter plane \sigma-\Delta \lambda, the non-single periodregions present asymmetric double-peak structure when \Delta \lambda > 0;the non-single period region number firstly increases and then decreaseswith the increase of \sigma .4. The route from periodic motion to chaos is via doubling-periodbifurcation.