![]() ![]() ![]() ![]() The dynamic responses of the system are presented numerically at the pick-up point A as the excitation frequency response ω l = 30 Hz, shown in Fig. The point A are used to locate the mid-span point of track structure (see Fig. In this section, the dynamic responses of the track structure under a variable speed moving harmonic load are illustrated numerically, including the amplitude-frequency response, the time-domain response, parameters effects on the dynamic behaviors.įirstly, two cases of uniform moving load and variable speeds moving load are considered respectively, i.e. Dynamic response analysis of track structures Secondly, the periodic analytical expressions for the dynamic response of arbitrary point on the track structures under a variable speed moving harmonic load is investigated, which is on the basis of the characteristics of the periodic structure’s response in frequency domain, and concretely analyze the influence of acceleration and initial velocity of the moving load on dynamic response of track structure.ģ. The analytical expression for the dynamic response of any point on the track structure under a variable speed moving harmonic load is efficiently derived consequently in the periodical scope. Firstly, the related problems of solving the track vibration response under mobile loads are transformed to solve a system of first-order equation of 4 variables in frequency domain by using the Fourier transform, is based on the fully consideration of the characteristics of the track structure itself. To make up these deficiencies, a vertical interaction model of a periodic track resting on infinite spans of elastically-supported girders is established in this paper to investigate the dynamic characteristics of track structures under a variable speed moving load. The literature review shows that existing investigations are mainly confined to the uniform condition of urban rail trains, and to the research on the Variable moving load is seldom addressed. But all the research cases always remained under the uniform moving load. modeled the rail as Euler beam on a two-parameter elastic foundation, and suggested that the random vibration response of the vertical coupled system of track was studied by the Green function method. However, the model only considered the vibration response under uniform moving load, and couldn’t solve the variable moving load. used the vibration theory to study the vertical dynamic response analysis model of Euler-Bernoulli beam under the arbitrary moving load columns. The urban rail transit area is shorter in our country currently, than the train is always in the state of variable speed in the transmission line. Many experts and scholars at home and abroad have paid close attention to it. With the rapid development of urban rail transit in our country, the vibration and noise caused by train operation are becoming more and more prominent. The vibration displacement response of the rail can be effectively improved by increasing the initial velocity of the moving harmonic load, while the peak value of amplitude-frequency response remained constant. The displacement response of the track increases slightly with increase of the acceleration, and the variation trend of dynamic response is basically similar. The research results indicate that the amplitude-frequency response peaks of the track under moving harmonic load with variable and constant speeds occur near the excitation frequency. Finally, the influences of velocity and acceleration on the dynamic response of track structure are numerically analyzed in detail. Based on the theory of the infinite periodic structure, the dynamic responses of the track structure under the variable speed moving harmonic load are analyzed theoretically. Secondly, for convenience of analysis, the analytical expression for the amplitude-frequency response of any point on the track structure under the moving harmonic load is derived in frequency domain. Firstly, the track is simplified as an Euler beam model periodically supported by continuous discrete point, the dynamic differential equation of vertical vibration for the track structure is formulated. Basing on the dynamic response characteristics of the periodic structure under a moving harmonic load in frequency domain and the superposition principle, the dynamic response of track structure under variable speeds moving harmonic load is investigated. ![]()
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