大跨度铁路桥梁变形弦测法评价的频域理论

Frequency Domain Theory of Chord Measurement to Evaluate the Deformation of Long-span Railway Bridges

为保障行车舒适性,需严格控制大跨度铁路桥梁的变形。从车辆加速度频响函数与弦测法频响函数相似性出发,提出桥上轨道线形评价的最优弦长选定原则,为大跨桥梁变形控制的弦测法提供理论依据。根据随机振动理论,推导弦测法矢度峰值与车辆加速度峰值之比(峰值比)的理论公式;然后,分析弦测法矢度与车辆加速度时程样本间的波形相似性,以及峰值比对轨道不平顺波长范围和功率谱函数的敏感性;最后,采用一座大跨度斜拉桥上的轨道线形实测数据检验峰值比的理论解。结果表明,最优弦长的弦测法矢度与车辆加速度波形相似性最高;二者峰值比对轨道不平顺的波长范围和功率谱函数都不敏感;以文中车速250 km/h的高速车辆为例,推荐以40 m作为最优弦长,弦测矢度和车辆加速度的峰值比平均值为11 mm·s^(2)/m。

The deformation of large-span bridges should be strictly controlled to ensure the riding comfort of railway vehicles. The optimal chord length to evaluate the track alignment on bridges is proposed by approximating the frequency response function of the vehicle’s acceleration by that of the chord measurement method, so as to provide some theoretical basis for the chord measurement method in controlling the deformation of long-span bridges. Firstly, based on the random vibration theory, the ratio of chord measurement’s peak to that of the vehicle acceleration is derived. Secondly, the similarity of time-domain waveforms between chord measurement results and vehicle acceleration is investigated;the sensitivity of the peak ratio to the wavelength range of track irregularity and its power spectral density is analyzed. Finally, the theoretical solution of the peak ratio is verified by the recorded rail irregularities on a cable-stayed long-span bridge. The results show that vector of the chord measurement using the optimal cord length is very close to the vehicle acceleration waveform, and the peak ratio using the optimal cord length is insensitive to the wavelength range and the power spectral density of the track irregularity. For the high-speed vehicle with a speed of 250 km/h in the paper, 40 m is recommended as the optimal chord length. The average value of the peak ratio of chord measurement and vehicle acceleration is 11 mm·s^(2)/m.