Abstract

Herein, an approach for the dynamic response of a four-beam system with arbitrary boundary conditions when subjected to successive moving loads is proposed. Based on the proposed method, the resonance condition of high-speed railway simply-support beam bridge with ballastless track-structure under moving train loads has been studied. Sine-Fourier series is an effective method that can play a key role in solving, particularly in transforming the infinite-degree-of-freedom four-beam system into a superimposed four-degrees-of-freedom system. The effect of boundary conditions of the track-structure on the dynamic response of the bridge was analyzed. It is concluded that obtaining the resonant speed of the bridge with ballastless track-structure via single-beam system is not the best route because the track-structure has an impact on the resonance characteristics of the bridges. Compared with previous studies, the four-degrees-of-freedom system obtained by proposed method greatly reduces the difficulty of calculating the natural vibration frequency. Thus, the resonant speed of any HSRSSBB could be quickly obtained, avoiding the dynamic response calculations. The analysis of the resonant speed conversion factor indicates that neglecting the track-structure can drastically overestimate the resonant speed of the bridge. The overestimation is particularly noticeable on the girders of lower mass, which are critical in engineering.

摘要

在此，提出了一种在承受连续移动载荷时具有任意边界条件的四梁系统的动态响应方法。基于该方法，对高速铁路无砟轨道结构简支梁桥在动车荷载作用下的共振条件进行了研究。正弦-傅里叶级数是一种有效的求解方法，尤其是将无限自由度四光束系统转化为叠加四自由度系统时，可以起到关键作用。分析了轨道结构边界条件对桥梁动力响应的影响。结论是通过单梁系统获取无砟轨道结构桥梁的共振速度不是最佳途径，因为轨道结构对桥梁的共振特性有影响。与以往的研究相比，本文方法得到的四自由度系统大大降低了自振频率的计算难度。因此，可以快速获得任何 HSRSSBB 的谐振速度，避免动态响应计算。谐振速度转换因子的分析表明忽略轨道结构会大大高估桥梁的谐振速度。高估在质量较低的大梁上尤为明显，这在工程中至关重要。所提方法得到的四自由度系统大大降低了自振频率的计算难度。因此，可以快速获得任何 HSRSSBB 的谐振速度，避免动态响应计算。谐振速度转换因子的分析表明忽略轨道结构会大大高估桥梁的谐振速度。高估在质量较低的大梁上尤为明显，这在工程中至关重要。所提方法得到的四自由度系统大大降低了自振频率的计算难度。因此，可以快速获得任何 HSRSSBB 的谐振速度，避免动态响应计算。谐振速度转换因子的分析表明忽略轨道结构会大大高估桥梁的谐振速度。高估在质量较低的大梁上尤为明显，这在工程中至关重要。谐振速度转换因子的分析表明忽略轨道结构会大大高估桥梁的谐振速度。高估在质量较低的大梁上尤为明显，这在工程中至关重要。谐振速度转换因子的分析表明忽略轨道结构会大大高估桥梁的谐振速度。高估在质量较低的大梁上尤为明显，这在工程中至关重要。