铁道学报
鐵道學報
철도학보
2015年
1期
97-104
,共8页
余志武%毛建锋%谈遂%曾志平
餘誌武%毛建鋒%談遂%曾誌平
여지무%모건봉%담수%증지평
车桥耦合模型%概率密度演化方法%列车随机参数%数论选点法%Voronoi区域
車橋耦閤模型%概率密度縯化方法%列車隨機參數%數論選點法%Voronoi區域
차교우합모형%개솔밀도연화방법%열차수궤삼수%수론선점법%Voronoi구역
train-bridge system model%probability density evolution method%random train parameters%num-ber theory collocation method%Voronoi area
车辆参数的随机性对车桥耦合随机振动的影响不可忽略。基于车-桥竖向耦合模型，考虑车辆荷载及一系、二系竖向弹簧刚度与弹簧阻尼的随机性，采用数论选点法对多维随机变量选取离散代表点，并基于正态分布利用 Voronoi区域对代表点集进行剖分赋得初始概率；建立概率密度演化随机动力方程，基于 MATLAB编制车桥耦合随机振动分析程序；采用 newmark-β积分法及带TVD格式的双边差分法计算车桥振动响应均值、标准差及时变概率密度演化分布。结果表明：与随机模拟法相比，概率密度演化法分析车桥随机振动精度更高，计算效率提高1~2个数量级；车辆载重随机荷载是车桥竖向耦合随机响应的主因之一；不可忽略二系竖向弹簧随机刚度及随机阻尼对列车竖向振动的影响；桥梁挠度均值整体随车速先增大后减小，其变异系数受车速的影响。
車輛參數的隨機性對車橋耦閤隨機振動的影響不可忽略。基于車-橋豎嚮耦閤模型，攷慮車輛荷載及一繫、二繫豎嚮彈簧剛度與彈簧阻尼的隨機性，採用數論選點法對多維隨機變量選取離散代錶點，併基于正態分佈利用 Voronoi區域對代錶點集進行剖分賦得初始概率；建立概率密度縯化隨機動力方程，基于 MATLAB編製車橋耦閤隨機振動分析程序；採用 newmark-β積分法及帶TVD格式的雙邊差分法計算車橋振動響應均值、標準差及時變概率密度縯化分佈。結果錶明：與隨機模擬法相比，概率密度縯化法分析車橋隨機振動精度更高，計算效率提高1~2箇數量級；車輛載重隨機荷載是車橋豎嚮耦閤隨機響應的主因之一；不可忽略二繫豎嚮彈簧隨機剛度及隨機阻尼對列車豎嚮振動的影響；橋樑撓度均值整體隨車速先增大後減小，其變異繫數受車速的影響。
차량삼수적수궤성대차교우합수궤진동적영향불가홀략。기우차-교수향우합모형，고필차량하재급일계、이계수향탄황강도여탄황조니적수궤성，채용수론선점법대다유수궤변량선취리산대표점，병기우정태분포이용 Voronoi구역대대표점집진행부분부득초시개솔；건립개솔밀도연화수궤동력방정，기우 MATLAB편제차교우합수궤진동분석정서；채용 newmark-β적분법급대TVD격식적쌍변차분법계산차교진동향응균치、표준차급시변개솔밀도연화분포。결과표명：여수궤모의법상비，개솔밀도연화법분석차교수궤진동정도경고，계산효솔제고1~2개수량급；차량재중수궤하재시차교수향우합수궤향응적주인지일；불가홀략이계수향탄황수궤강도급수궤조니대열차수향진동적영향；교량뇨도균치정체수차속선증대후감소，기변이계수수차속적영향。
The influence that the randomness of train parameters has on the train-bridge coupled random vibra-tion cannot be ignored.Based on the train-bridge vertical coupled model and considering the randomness of a few train parameters including the train load,the stiffness and damping of primary suspension and secondary suspension,,this paper selected the disperse representative points from multi-dimensional random variables by utilizing the number theory collocation method,and subdivided the joint probability density of representative points of Voronoi area according to normal distribution,thus obtaining the initial probability assignment.Then the random dynamic equation for probability density evolution method was established,and by using MAT-LAB,the program for analysis of train-bridge coupled random vibration was developed.Eventually,the new-mark-βintegration method and the double edge difference method of TVD format were adopted to obtain the mean value,the standard deviation and the distribution of the time dependent probability density evolution. Results show that compared to the Monte Carlo method,the probability density evolution method has a higher accuracy and computation efficiency,with efficiency being improved by 1~2 order of magnitudes.The results also verify that the random load of vehicle body is one of the maj or causes that incur train-bridge random vibra-tion.The effects that the random stiffness and damping of secondary suspension has on the train vertical vibra-tion should not be neglected.The bridge deflection mean first increased and then decreased with train speed. The coefficient of variation of bridge deflection was affected by train speed.
