考虑时变特性的车-桥耦合系统非平稳振动频域方法研究  

Frequency-domain method of non-stationary vibrations of time-varying train-bridge coupled system

作　　者：雷思勉 葛耀君[1] 李奇[1] LEI Simian;GE Yaojun;LI Qi(College of Civil Engineering,Tongji University,Shanghai 200092,China;DICAM,University of Bologna,Bologna 40121,Italy)

机构地区：[1]同济大学土木工程学院,上海200092 [2]博洛尼亚大学土木工程学院,意大利博洛尼亚40121

出　　处：《铁道科学与工程学报》2024年第5期1930-1941,共12页Journal of Railway Science and Engineering

基　　金：西藏自治区自然科学基金重点项目(XZ202301ZR0040G);国家自然科学基金资助项目(52178432,51978527)。

摘　　要：当列车行驶经过桥梁时,由于车辆在桥上的位置随时间不断变化,车-桥耦合系统具有时变特性,即使假设轨道不平顺为平稳激励,车辆和桥梁的振动仍然是一种非平稳的随机过程。本研究旨在提出一种非平稳频域分析方法,以高效分析受轨道不平顺激励的车-桥耦合系统的非平稳随机振动问题。首先推导了单节列车通过单跨简支桥的耦合系统时变频响传递函数(FRF),据此描述线性时变系统的动力特性。该函数满足一组变系数微分方程,可采用摄动法求解该函数,从而提高计算效率。随后,结合PRIESTLEY的演化谱理论,推导非平稳随机响应的演化功率谱密度函数(EPSD)。基于非平稳频域分析方法,计算响应时变均值和方差,结合3σ准则来估计非平稳响应的极值。研究结果表明,由于轨道不平顺的影响,车辆振动表现出平稳随机过程的特性,但其方差较大,表现出更大的离散性;而桥梁的振动则呈现出明显的非平稳特性,但方差较小,响应具有较小的随机性。极值分析表明,轨道不平顺激励对车辆振动具有显著影响,其均方根对极值响应起主导作用。而轨道不平顺激励对桥梁振动的影响较小,桥梁振动则主要受移动质量影响,其响应的极值主要受均值的影响。此外,相较于系统位移响应,车速对加速度响应的影响更为显著,例如车身加速度响应最大值随车速的增加可增大至3倍左右。Vibrations of a moving vehicle and the coupled bridge are non-stationary stochastic processes due to the time-dependent characteristic of the coupled vehicle-bridge system.The study aimed to present a frequency domain method to calculate the non-stationary vibrations of the coupled vehicle-bridge system excited by track irregularities.As an example of application of the method,a simply supported Euler beam traversed by a single railway vehicle was considered to represent the coupled system.The time-dependent frequency response function(FRF)was first derived to characterise the linear time-varying system.The perturbation method was adopted to improve the calculation efficiency.With the help of Priestley’s Evolutionary Spectra theory,the evolutionary power spectral density(PSD)of the system response was then derived.Based on the proposed method,the timevarying standard deviation and mean of the response were conveniently obtained,and thus the 3σrule can be adopted to estimate the extreme values of the non-stationary response.It proves that the vehicle response can approximately be regarded as stationary but with large variance arising from the random track irregularities.In contrast,the bridge vibration follows a strongly non-stationary process with small randomness.Moreover,it is found the train speed has a significant effect on the non-stationary acceleration of coupled system.

关 键 词：车桥耦合 轨道不平顺 频域分析方法 非平稳随机振动 摄动法 演化谱 

分 类 号：TU29[建筑科学—建筑设计及理论]