移动谐振荷载作用下曲线轨道钢轨动力响应求解方法研究

Solving method for curved track dynamic responses under a moving harmonic load

将曲线轨道视作周期性轨道结构,根据周期性结构的振动特性,可将荷载作用下曲线轨道钢轨动力响应的求解问题转化在一个基本元之内进行。通过引入移动谐振荷载作用下曲线轨道钢轨的数学模态,得出了曲线轨道钢轨频域响应的级数表达。在频域内采用模态叠加法表示钢轨的弯曲及扭转变形,进而求解得出钢轨的频域动力响应。经研究发现:移动荷载作用下曲线轨道钢轨响应显著的频段位于荷载激励频率附近,随着荷载移动速度的增加,荷载激励频率附近一个很窄频段内的位移响应将有所减小,但其它大部分频段内的位移响应将显著增大;随着荷载移动速度的增加,移动谐振荷载引起的钢轨响应峰值变化不大,但响应显著的持续时间变短;离散支承引起的参数激励受速度的影响显著;采用曲线梁模型模拟曲线轨道钢轨所得垂向动力响应结果与直梁模型基本一致,可以采用直梁模型近似研究曲线轨道钢轨垂向动力响应;当对曲线轨道钢轨进行精细化建模分析时,曲线半径对曲线钢轨扭转振动有一定程度的影响,需采用曲梁模型研究曲线轨道钢轨动力响应。

How to model a curved railway track subjected to a moving harmonic load is very important to solve its dynamic responses.Here,a periodically supported discrete curved Euler-Bernoulli beam was used to simulate dynamic responses of a curved track taken as a part of a circular structure periodically supported.The problem to solve dynamic responses of a curved track could be changed into one to be solved within one basic cell of track based on the dynamic property of periodic structures subjected to moving harmonic loads.Through introducing a curved track’s vibration modes and using the modes superposition method in frequency domain,its dynamic response was expressed with a series of its bending modes displacements and torsional ones in frequency domain.The study results showed that frequency ranges for significant dynamic responses of a curved track under a moving harmonic load are near load excitation frequencies;with increase in the moving speed of load,the track’s displacement responses decrease within a very narrow range near load excitation frequencies,but the track’s displacement responses within most parts of the other frequency ranges obviously increase;with increase in the moving speed of load,the peaks of the track’s responses change little,but time durations for significant responses become shorter;the effect of load moving speed on discrete supports’parametric excitation is significant;the vertical dynamic responses of the curved track obtained with a curved beam model agree well with those obtained with a straight beam one,so a straight beam model can be adopted to approximately study the vertical responses of the curved track;when the curved track was analyzed with a precise model,curve radius has a certain effect on the track’s torsional vibration,so a curved beam model is needed to study the curved track’s dynamic responses.