Study On Dynamic Response And Mechanism Of High-speed Trains Subjected To Crossing Air Pressure Pulse

With the development of high-speed train, many aerodynamic problems, which have been neglected when trains ran at low speeds, are being raised with drawing researchers’ attentions. The aerodynamic problems mainly are aerodynamic drag problem, cross-wind effects, wind tunnel effects and effects due to trains passing each other, etc. Available researches about the effects due to trains passing each other contain three aspects, basic characteristics of crossing air pressure pulse, the influence of crossing air pressure on the stability of train running and the influence of crossing air pressure on the train body and side windows. The studies on the third aspect are limited to evaluate the safety of train body and side windows subjected to pressure pulse with the model of side windows or part of train body. That method of safety evaluation will not bring large error for the trains running at low speed. But, for the speed-up of train with lighter of train body, it will be lack of consideration of the effect of dynamic response of whole train body on the safety of train body and side windows. The paper focused on studying the dynamic response of whole train body when high-speed train subjected to the crossing air pressure, and the effect of that response on the safety of side windows. The dynamic response of middle carriage subjected to crossing air pressure and the safety evaluation of side windows under that load were investigated by using finite element method. Then, the characteristics and mechanisms of dynamic response of train body subjected to crossing air pressure by analyzing a simplified model with the methods of finite element method and theory model. Main work and findings include:(1) Finite element analysis of dynamic response of side windows of high-speed trains subjected to crossing air pressureTwo kinds of finite element models of the middle carriages of CRH2and CRH3were built, the loading conditions contained in the models:moving air pressure pulse, uniform dynamic load and static load. Through the study of CRH2model, it was found that the peak stresses side window centers were lower than the other two loading conditions. When the traveling velocity of trains is lower, the peak stresses of side window centers calculated under uniform dynamic load are higher than those of the other two loading situations. As the velocity increases, the peak stresses of side window centers resulted by the moving air pressure pulse exceed those calculated under uniform dynamic load. Hence, the influence of crossing air pressure pulse caused by high-speed trains passing each other must be considered when elevating the safety of side windows. Through the study of CRH3model, it was found that the results were similar with those of CRH2. The differences between two models are that, in the CRH3model, the peak stresses of side window centers calculated under uniform dynamic load are higher than those of the moving air pressure pulse at a higher traveling speed than those in CRH2, and the relative error of peak stress of side window centers between the loading conditions of uniform dynamic load and moving air pressure pulse is6%. The peak stresses of side window centers can be used for the safety evaluation of side windows subjected to crossing air pressure pulse.(2) Finite element analysis of semi-infinite beam to a moving pulseDue to the complexity of the structure of train body, it’s very difficult to investigate the flexural wave travelling in the structure. A simplified model was built in this chapter, i.e., the finite element model of semi-infinite beam to a moving single sinusoidal pulse was built. For an identical pulse duration, there exists a critical velocity, i.e., the the average value of maximal equivalent stress in the beam reaches its maximum value when the velocity of moving pulse is closed to a critical velocity. The critical velocity decreases as the pulse duration increases. The average value of maximal equivalent stress in the beam increases as the pulse duration increases when the moving pulse moves at critical velocity. The position where the maximum degree of bending appears moves away from the region of moving pulse applied. The mechanism of stress fluctuation was also studied. The material, structural and load parameters influencing the critical velocity were analysed with dimensionless analysis. An empirical formula of the critical velocity with respect to the speed of elastic wave, the gyration radius of the cross-section and the pulse duration was obtained.(3) Theoretical analysis of semi-infinite or infinite beam to a moving pulseDue to limitation of the numerical method, in this chapter, the method of theoretical analysis was used to study the simplified model. Based on the Bernoulli-Euler beam theory, the theory model of the semi-infinite beam to a moving pulse was built and solved by Fourier transform. The transient solutions of displacement and stress of semi-infinite beam to a moving pulse were obtained. The effectiveness of the theoretical solution was verified by comparing the displacement of beam with the result of FEA. The variation trend of the maximum stress in the beam changing with time is the same to the distance between the position of maximum stress and the front of moving pulse changing with time. Also based on the Bernoulli-Euler beam theory, the theory model of the infinite beam to a moving pulse was built and solved by Green function, two-dimensional Fourier transform and theorem of residue. The explicit steady-state solutions of displacement and stress of infinite beam to a moving pulse were obtained. For an identical pulse duration, the critical velocity was also found. Comparing it with the critical velocity of transient solution and the speed of harmonic wave whose period is equal to the pulse duration, it was found that the critical velocity of steady-state solution is much closer to the critical velocity of transient solution than the speed of harmonic wave. The expression of the lateral distance of vibration equilibrium positions between the front and behind loading area for the steady-state solution can be a good characterization of the deflection behind the loading area for the transient solution. They are both not affected by the velocity of moving pulse. The approximate solution of critical speed for the steady-state solution was obtained, and it was consistent with the critical speed for the transient solution well. The dynamic response of beam to a crossing air pressure pulse was obtained by modified the above solutions with the characters of crossing air pressure pulse. For the identical trains passing each other, i.e., the length of crossing air pressure pulse is constant, the critical velocity was also found. For constant coefficient of the amplitude of crossing air pressure pulse and the square of velocity trains passing each other, the maximum stresses in the beam are uniform for different lengths of crossing air pressure pulse when the crossing air pressure pulse moves at critical velocity.