考虑塔梁影响的斜拉索随机激励参数振动分析

Random Excitation Parameter Vibration Analysis of Stay Cable Considering the Influence of Tower Beam

为了揭示随机激励下斜拉索参数振动特性,考虑塔、梁协同振动的影响,建立了高斯白噪声激励下斜拉索-桥塔-桥面梁耦合振动微分方程,推导了耦合体系的伊藤状态方程组,采用Milstein-Platen法构造了斜拉索振动时程求解迭代格式,研究了斜拉索振动的时程、统计和频域特性,分析了桥塔侧向扶正作用、激励强度和索塔梁初始位移对拉索振幅产生的影响.结果表明:随机激励下斜拉索振动呈现出双“拍”振现象,“拍”幅值和周期具有随机性;拉索随机位移均值、均方差在振动初期具有长时间的非平稳特性;拉索响应幅值对应的频率和拉索功率峰值对应的频率基本一致,但随机激励下的拉索幅值和功率峰值更大;拉索振动概率密度曲线满足高斯分布和马尔科夫性质;桥塔侧向扶正作用越强,拉索振幅越小;激励强度越小,拉索振幅越小;各结构初始位移越大,拉索振幅越大,且对桥面梁初始位移越敏感.

In order to reveal the vibration characteristics of stay cables under random excitation,the differential equations of cablepze-deck beam coupling vibration under Gaussian white noise excitation were established.The ITO state equations of coupling system were derived,and the iterative solving scheme of cable-stayed vibration time history was constructed by Milstein-Platen method.The time history,statistics and frequency domain characteristics of the vibration of the cable were studied.The influences of the lateral righting action from the bridge tower,the excitation strength and the initial displacement of cable tower beam on the amplitude of the cable were analyzed.The results show that the vibration of the stay cable presents a double"beat"phenomenon under random excitation,with random"beat"amplitude and period.The mean value and mean square error of the random displacement from the cable are non-stationary for a long time at the initial stage of vibration.The frequency corresponding to the cable response amplitude is basically the same as the frequency corresponding to the cable power peak,but the cable amplitude and power peak are larger under random excitation.The probability density curve of cable vibration satisfies the Gaussian distribution and Markov properties.The stronger the lateral righting of the pylon,the smaller the amplitude of the cable.The smaller the excitation strength is,the smaller the cable amplitude is.The larger the initial displacement of each structure,the larger the amplitude of the cable,and the more sensitive it is to the initial displacement of the bridge deck beam.