基于谐波平衡法的斜拉索-非线性减振系统振动特性研究

Stay cables, as significant structural members in cable-stayed bridges, are vulnerable to ambient excitations owing to its extremely low inherent damping, posing a threat to the bridge safety. Installing near-anchorage damper is among the most effective countermeasures for cable vibration control. To include the nonlinearity of real-world dampers and further explore the advantage of nonlinear control for improving cable vibration mitigation, this project intends to conduct dynamic analysis and parameter optimization of a cable attached with a nonlinear control device. Firstly, steady-state responses, which represent a significant subset of the dynamics of a nonlinear system, will be focused on for the concerning system; harmonic balance method (HBM) which is undergoing rapid development in fields such as mechanical engineering and capable of efficiently handling strong nonlinearity, will be introduced and accommodated to deal with the multi-degree-of-freedom cable systems. Secondly, research effort will be dedicated to the development of appropriate approaches for appreciating the control effect of the nonlinear device based on system steady-state responses. Eventually, a HBM-based methodology will be established for dynamic analysis and parameter optimization of the cable under nonlinear control. Furthermore, using this method, typical nonlinear devices including nonlinear viscous damper, friction damper and lateral contactor will be analyzed in detail for maximizing cable vibration control effect; nonlinear control mechanism will be revealed meanwhile. The results of this project can be directly used for cable vibration control design and provide a theoretical framework for exploring new control schemes. In other words, this project is of both practical and theoretical significance.

斜拉索是斜拉桥的关键受力构件，其自身阻尼很小因而易在环境激励下发生振动，危及斜拉桥的安全。在索近锚固点安装减振器是最有效的减振方法。为了研究实际索减振器的非线性行为并利用其在拉索减振中的优势，本项目拟研究斜拉索-非线性减振系统的动力特性及参数优化方法，将关注该系统的重要动力特性--稳态响应。首先，拟引入近来在机械等领域快速发展、能高效求解强非线性系统的谐波平衡法，研究该方法在分析索减振系统这一多自由度结构中的适用性；进而，研究基于系统稳态动力特性评价其减振性能的合理方法；最终，建立基于谐波平衡法的拉索-非线性减振系统的动力分析及参数优化框架。拟利用该方法，具体分析非线性粘滞阻尼器、摩擦阻尼器及限位装置安装于索近锚固点时对索前几阶振动的最优控制效果及相应装置参数，探讨非线性减振机理。本课题的成果将直接应用于拉索减振装置的优化设计，为索减振方案的开发提供理论基础，具有明确的工程和理论价值。

工程实际中的索常安装粘滞阻尼器和摩擦阻尼器进行减振，这两种阻尼器的力学特性均表现出明显的非线性。为了研究斜拉索-非线性系统的振动特性、明确其减振耗能机理，进而优化设计阻尼器的参数，本项目提出了基于索-非线性阻尼器强迫振动响应评价其阻尼效果的方法。首先，项目对文献中基于模态展开和拟静力修正的索-阻尼器数值模型进行改进，使其采用正交的基函数，提高近共振分析精度；此外，拓展方法使其能考虑单根索附加多个阻尼器的情况。然后，基于索的数值模型，建立了索周期性响应分析的谐波平衡方法，并结合数值延拓方法使其能快速求解索-阻尼器系统在其共振频率附近的频响函数；最后，基于频响函数提出了非线性阻尼器对索附加阻尼的等效估计方法。建立的索-阻尼器分析和阻尼评价方法，首先应用于线性阻尼器的情况，得到的阻尼曲线等结果与复模态分析结果吻合，验证了建立的方法的有效性。进而，采用建立的方法详细分析了非线性粘滞阻尼器和摩擦型阻尼器对张紧索(忽略垂度)的阻尼效果，研究了阻尼器的非线性参数、阻尼器的安装位置和索的振动模态对非线性阻尼器阻尼效果的影响，进而分析了非线性阻尼器的减振机理。结果表明，最优情况下非线性阻尼器的阻尼效果优于最优线性阻尼器的阻尼效果，因为非线性阻尼器能引起索的高阶振动，从而索振动能量向高阶转移并快速耗散。项目进而分析了垂度效应对非线性阻尼器阻尼效果的影响，发现当垂度很小时，最优情况下非线性阻尼器优于线性阻尼器；当垂度参数增大后，最优线性阻尼器优于最优非线性阻尼器；垂度大于一定值以后，最优情况下，两种阻尼器阻尼效果相当。项目还分析了垂索在其两端对称安装两个非线性粘滞阻尼器后，系统最优阻尼和最优阻尼器参数随垂度参数变化的变化。最后，项目以苏通大桥一根长索为目标，设计了黏性剪切阻尼器并开展了单体试验，单体试验结果表明其力学特性具有非线性；然后将阻尼器安装在目标索上进行了单点周期性荷载强迫振动试验，对比试验测得的索稳态响应和采用项目建立的模型进行模拟分析的结果，初步验证了建立的模型的准确性；对比基于强迫振动评价得到的阻尼和基于自由衰减响应得到的阻尼，初步验证了项目提出的非线性阻尼器阻尼评价方法的适用性。

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