Due to their low inherent damping and high lateral flexibility, stay cables are prone to large amplitude vibrations governed by either a single or multiple cable modes. Among the practical measures, the installation of transverse passive dampers near the cable‐deck anchorage is a popular choice. Compared to conventional positive stiffness and zero stiffness dampers, negative stiffness damper (NSD) manifests superior performance in mitigating cable vibrations, especially in the case of long cables. In this study, a novel design approach is proposed to optimize NSD for multimode cable vibration control. Two design scenarios are considered. In the former, the damper size is optimized for a predetermined negative damper stiffness; whereas in the latter, the size and negative stiffness of the NSD are both optimized to achieve a required damping ratio for the dominant modes. The applicability of the proposed NSD optimum design approach is validated using 15 sample real stay cables. A numerical example is presented, of which a NSD is designed based on the proposed approach to optimize wind‐induced multimode vibration control of a 460‐m stay cable, and the performance is compared with that of a linear‐quadratic regulator (LQR) control. Results show that the selected NSD can effectively suppress the dominant modes and has a controlling effect comparable with an active control using LQR. In addition, it is found that when there exist more than two dominant modes in vibration, designing NSD for the lowest and the highest dominant modes would also adequately control the mid‐range modes.

中文翻译：

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使用优化的负刚度阻尼器的斜拉索多模振动控制

由于其固有的低阻尼和较高的侧向柔韧性，斜拉电缆易于受到由单电缆或多电缆模式控制的大振幅振动的影响。在实际措施中，在电缆桥面锚固点附近安装横向无源阻尼器是一种普遍的选择。与传统的正刚度和零刚度阻尼器相比，负刚度阻尼器（NSD）在减轻电缆振动方面表现出优异的性能，尤其是在长电缆的情况下。在这项研究中，提出了一种新颖的设计方法来优化用于多模电缆振动控制的NSD。考虑了两种设计方案。在前者中，阻尼器的尺寸针对预定的负阻尼器刚度进行了优化。而在后者中，NSD的尺寸和负刚度都经过优化，以实现主导模式所需的阻尼比。NSD最佳设计方法的适用性通过15条样本实心电缆进行了验证。给出了一个数值示例，其中基于建议的方法设计了NSD，以优化460 m斜拉索的风致多模振动控制，并将其性能与线性二次调节器（LQR）控制进行了比较。结果表明，所选择的NSD可以有效地抑制主导模式，并且具有与使用LQR的主动控制相当的控制效果。此外，发现在振动中存在两个以上主导模式时，为最低和最高主导模式设计NSD也将适当地控制中频模式。