斜拉桥风振减振基于H_2范数的ATMD和传感器配置优化

Optimal placement of ATMD and sensors based on H_2-norm for wind response control of cable-stayed bridge

斜拉桥在风荷载作用下易出现多模态参与的大幅振动,宜采用主动式ATMD(active tuned mass damper)减振。针对斜拉桥风振减振设计中的ATMD及传感器的位置和数量配置问题,在建立风荷载作用下斜拉桥与ATMD组合系统模型的基础上,用模态坐标表示H2范数,提出包括外激励影响的分别针对作动器和传感器配置优化的H2范数指标,推导ATMD对结构的共振激振模型,考虑ATMD和加速度传感器的动力性能并对配置指标进行修正,建立能够以开环方式有效实现ATMD和加速度传感器配置的优化方法。以南京长江第三大桥的风振减振为例,定量分析ATMD和加速度传感器的优化位置和数量。结果表明,采用考虑外激励权重的H2范数指标,并结合考虑ATMD动力性能,能够有效实现针对结构多模态参与的风振减振的ATMD和加速度传感器的配置优化。

For cable-stayed bridges,large amplitude multi-mode vibrations are easily induced by wind loads,and active tuned mass dampers( ATMD) have proved effective in the vibration control. To resolve the placement problem of ATMD and sensors utilized for the wind response control of cable-stayed bridge,a mathematical model for the combined system of ATMD and cable-stayed bridge under wind loads is established. By expressing the H2-norm of the combined system with modal coordinates,the H2-norm index is put forward,respectively,for the placement of ATMD and sensors with the influence of exterior excitation considered. Furthermore,a model for the resonance of the bridge structure under ATMD excitation is deduced. By considering the dynamic behaviors of ATMD and acceleration sensor,the H2-norm indexes are modified,and then the optimal method for the placement of ATMD and sensors is proposed based on the open-loop optimization. By taking the 3rd Nanjing Bridge over Yangtze River under construction as an example,the optimal locations and numbers of ATMD and sensors are quantitatively analyzed for the wind response control. Results show that by using the H2-norm indexes with the dynamic characteristic of ATMD considered,the locations of ATMD and sensors can be effectively optimized for the multi-mode vibration control.