研究了亚音速流中二维壁板在外激励作用下的分岔和响应问题.采用Galerkin方法将非线性运动控制方程离散为常微分方程组.采用Runge-Kutta数值方法进行了数值计算,研究了壁板系统非单周期区在参数空间的分布情况.结果表明：在参数空间中,非单周期区和单周期区会交替出现;在不同的单周期区内,系统运动轨线也在有规律的变化;系统由单周期运动进入混沌运动是经过一系列周期倍化分岔产生的.%Along with the development of high speed multiple unite train and intercity railroad,the high speed technology has become the development direction of train.With the increase of speed,the aerodynamic problems of such train are emerging,while neglected in low speed.Future trains will increase their speeds substantially,and if so,aerodynamic forces may influence train running safety and affect passenger＇s comfort. So the aeroelasticity of high speed train is the problem to be urgently and promptly solved.Because the high speed train adopts stream line design to decrease running resistance,lots of panel structures such as body skin are widely used.When train runs with lower speed,these panel structures will vibrate with small amplitude and can not be inhibited at all.But under combined aerodynamic forces and wheel-rail excitation,complicated aeroelasticity phenomena of these panel structures may occur. The bifurcation and responses of two-dimension panel with external excitation in subsonic flow are studied in this paper.Based on the potential theory of incompressible flow,the aerodynamic pressure for air acting on the top side of the panel is acquired.The wheel-rail excitation is simplified as external forcing acting on the panel.The cubic stiffness and viscous damper in middle of the panel are considered.The nonlinear governing motion equations are reduced to a series of ordinary differential equations by the Galerkin method.The Runge-Kutta numerical method is used to conduct numerical simulations.The distribution of non-single period areas of the panel system are indicated in differential parameter planes.The effect of three dimensionless parameters, namely viscous damping coefficientσ,external forcing amplitudeβand dynamic pressure incrementΔλ,is emphatically investigated. The results of this paper show that the pitchfork bifurcation occurs with the increase of dynamic pressure, and the number and stability of the equilibrium points change after the dynamic pressure exceeds the critical value.In differential single period regions,the system motion trajectories in phase-plane portraits change rhythmically. 1.In the parameter planeσ-β,the number of non-single period regions decreases with the increase ofσ; the non-single period regions and single period regions appear alternately with the increase ofβ. 2.In the parameter planeΔλ-β,the non-single period region number firstly increases and then decreases with the increase ofΔλ;the non-single period regions and single period regions appear alternately with the increase ofβ. 3.In the parameter planeσ-Δλ,the non-single period regions present asymmetric double-peak structure whenΔλ0;the non-single period region number firstly increases and then decreases with the increase ofσ. 4.The route from periodic motion to chaos is via doubling-period bifurcation.
展开▼
