轨道不平顺激励下车辆-桥梁垂向随机振动方差解法

提出时滞多维非白噪声轨道不平顺激励下车辆-桥梁垂向随机振动的时域分析方法。采用白噪声滤波法模拟单轮对下的不平顺,在宽频带内识别滤波器参数以实现波长选择功能。基于Pade近似构造累次时滞滤波器以反映各轮对下不平顺之间的时滞关系。结合成型和时滞滤波器,构造以一致白噪声为输入、时滞多维非白噪声不平顺为输出的合成滤波器。建立车辆-桥梁垂向振动模型,并与合成滤波器联立得到一致白噪声激励下的车-桥-滤波器扩阶状态方程。继而提出求解此扩阶时变系统随机振动方差响应的递推算法。算例结果与MonteCarlo模拟法符合良好,表明该方法具有足够的精度,且对时间步长不敏感。

Covariance Method for Vehicle-bridge Vertical Stochastic Vibration Excited by Rail Irregularities

A time domain method was proposed for analyzing the vehicle-bridge stochastic vibration excited by multidimensional time-delay nonwhite rail irregularities.The rail irregularity under a single wheelset was produced by the white noise filtration method.And the parameters of the shape filter were identified in a wide frequency range to realize wavelength selection.Based on the high order Pade approximation,a stepwise time-delay filter was constructed to reflect time-delays among irregularities under different wheelsets.A combined filter with uniform white noise input to generate multidimensional time-delay nonwhite rail irregularities was constructed by combining the shape filter and the time-delay filter.The vehicle-bridge vertical dynamic model was established,and was integrated into the combined filter to obtain the expanded order vehicle-bridge-filter state-space equation.Then,a covariance recursive method for the stochastic vibration analysis of the expanded time-variant system was suggested.Numerical results accord well with the Monte Carlo simulation method,which indicates the high accuracy of the proposed method.In addition,the method shows no sensitivity to the time step size.