Complex Nonlinear Response Study Of High-Speed Train Aeroelastic System

This dissertation mainly presented some basic aeroelastic problems in a high-speed train system. The related researches mainly consist of two parts:one is on the subsonic aeroelastic stability and the nonlinear dynamics of panel structures used for high-speed train, and the other is on the lateral stability and the nonlinear responses of high-speed vehicle based on the theory of aeroelasticity, and the flow-induced vibrations during high-speed train running. The main contributions of this dissertation are as follows:1. The stability of a two-dimensional panel in subsonic flow is investigated. Firstly, the aerodynamic force acting on the top side of a panel is obtained based on the incompressible potential theory and the stability of the panel with different boundary conditions is studied by differential quadrature (DQ) method. Then, the governing equations of both subsonic compressible flow and two-dimensional elastic panel are discretized by using DQ method at the same grid points, and the instability of the fluid-panel system is analyzed by eigenvalue theory. The results show that the panel which is fixed at both ends (simply supported or clamped) undergoes divergence and the critical divergence dynamic pressure of clamped panel is higher than that of the simply supported one. The flutter phenomenon exists in the panel with clamped-spring support and the critical flutter dynamic pressure is influenced by some system parameters.2. The aeroelastic stability and bifurcation structure of a panel exposed to subsonic flow and subjected to external excitation is investigated. The von Karman’s large deflection equations of motion for a flexible panel and Kelvin’s model of structural damping is considered to derive the panel governing equation. The panel under study is two-dimensional and simply supported. A Galerkin-type solution is introduced to derive the unsteady aerodynamic pressure from the steady linearized potential equation of uniform compressible flow. The aeroelastic stability of the linear panel system is presented in a qualitative analysis and numerical study. The numerical simulations are used to investigate the bifurcation structure of the nonlinear panel system and the distributions of chaotic regions are shown in the different parameter spaces. The results show that the panel under study loses its stability by divergence not flutter; the number of the fixed points and their stabilities change after the dynamic pressure exceeds the critical value; the chaotic regions and periodic regions appear alternately in parameter spaces; the single period motion trajectories change rhythmically in different periodic regions and the periodic regions present notable scaling property; the route from periodic motion to chaos is via period-doubling bifurcation; the symmetric single period motions lose their symmetry and become asymmetric single period motions firstly before they go into chaotic region.3. Based on the potential theory of incompressible flow and the energy method, a two-dimensional simply supported thin panel subjected to an external forcing and uniform incompressible subsonic flow is theoretically modeled. The nonlinear cubic stiffness and viscous damper in the middle of the panel is considered. The Galerkin method is adopted to discrete the governing partial differential equations. The stability of the fixed points of the panel system is analyzed. The regions of different motion types of the panel system are investigated in different parameter spaces. The rich dynamic behaviors are presented as bifurcation diagrams, phase-plane portraits, Poincare maps and maximum Lyapunov exponents based on carefully numerical simulations. The results show that there is no Hopf bifurcation (flutter) for the present model; the pitchfork bifurcation (divergence) occurs with dynamic pressure increases; the number of the fixed points and their stabilities will change after the dynamic pressure exceeds the critical value; the multi-fixed points structure as a result of the change of dynamic pressure has very important influence on the system dynamic behaviors; the periodic windows and chaos occur alternately in the analysis of complicated responses in one non-single period region; the period-n (n=3,5,7,9) motions exist; the route to chaos is via period-doubling bifurcation and the route from chaos to periodic motion is intermittency.4. Melnikov’s method is adopted to study the chaotic vibrations and the chaos control of a two-dimensional nonlinear thin panel subjected to subsonic flow and external excitation. The Galerkin method is used to transform the governing partial differential equation into a series of ordinary differential equations. By using the Melnikov’s method, the chaotic behaviors and implement chaos control by adding a parametric excitation term to the chaotic system are analyzed. The results show that the number and stability of the fixed points of the unperturbed Hamilton system change after the dynamic pressure exceeds the critical value, and then the homoclinic orbits appear and will result in chaos by the Smale-Birkhoff theorem under the weak periodic perturbation; the use of the Melnikov’s method for the chaos and its control of the panel is reasonable.5. The stochastic behavior of the nonlinear panel subjected to subsonic flow with pressure fluctuations and an external forcing is studied. The panel under study is two-dimensional and simply supported. The aerodynamic pressure is considered as the sum of two parts, one given by the pressure fluctuations on the panel in the absence of any panel motion, and the other due to the panel motion itself which can be derived from the potential theory. The random pressure fluctuations are taken as the Gaussian white noise. Transformation of the governing partial differential equation into a set of ordinary differential equations is performed through the Galerkin method. The closed moment equations are obtained by the Ito differential rule and Gaussian truncation. The stability and complex different responses of the moment equations are studied. The results show that the pitchfork bifurcation occurs in the panel system and the bifurcation point is consistent with the system without pressure fluctuations; the chaotic response regions and the periodic response regions appear alternately in parameter spaces; the periodic responses trajectories change rhythmically; the route from periodic response to chaos is via period-doubling bifurcation.6. Based on the von Karman’s large deflection theory and the energy method, the governing equation of a three-dimensional panel in uniform subsonic flow subjected to an external forcing is theoretically modeled. The panel is simply supported and the Kelvin’s model of structural damping is also considered. The Galerkin method is used to derive the aerodynamic pressure from the two-dimensional potential equation. The stability is analyzed, and the nonlinear dynamic behaviors are presented as bifurcation diagrams, phase-plane portraits, Poincare maps based on carefully numerical simulations. The results show that the panel loses its stability by divergence not flutter; the nonlinear panel can undergo many types of bifurcations namely:symmetry breaking bifurcation, saddle-node bifurcation, period-doubling bifurcation, inverse period-doubling bifurcation; the symmetric single period motions lose their symmetry firstly before they go into chaotic motions and the chaotic regions and the periodic regions appear alternately; many sudden period-n (n=3,5,7,9) motions appear in chaos; the route to chaos is not only via period-doubling bifurcation but also quasi-period and intermittency; the route from chaos to periodic motion involve inverse period-doubling bifurcation and intermittency.7. From the viewpoint of aeroelasticity, the governing differential equations of a high-speed vehicle model with seventeen degrees of freedom are derived under the supposition of quasi-steady aerodynamic force. The influence of aerodynamic force on the critical hunting speed and the curve negotiation performance are analyzed. The limit cycle motions of the nonlinear system with flange force and aerodynamic force are studied. And then a simplified model of a high-speed train consisting of three cars (leading car; middle car and tail car) is used to calculate the aerodynamic force by numerical simulation. The responses of the train considering aerodynamic load are analyzed. The results show that the aerodynamic force has great influence on the hunting speed of high-speed vehicle when the secondary lateral stiffness is smaller; the aerodynamic force increase the lateral and yaw displacement of high-speed vehicle during the curve negotiation, however, the effect on the wheel lateral displacement is not obvious; the aerodynamic force affect the behaviors of limit cycle of the nonlinear vehicle system obviously, reducing the critical instability speed and changing the instability characters; the aerodynamic force has obvious effect on the vehicle system dynamic behaviors when trains passing with equal speed on the ground, the responses of the leading and tail car are most significant; the higher passing speed is, the more intense the responses of vehicle system are, and the responses of trains with different hunting speed are significantly different; the cross wind has important effect on the vehicle system dynamic behaviors, the most serious responses can be found at the leading car, followed by the middle and tail ones; with the same cross wind speed, the responses of vehicle system running at higher speed are more intense; at the same running speed, the responses of vehicle system in higher-speed cross wind are more intense; the responses of trains with different hunting speed in cross wind are significantly different;...