Optimized negative stiffness damper with flexible support for stay cables

The negative stiffness damper (NSD) has been gaining increasing attention for cable vibration control owing to its superior energy dissipation capacity. Recent research has implied that a flexible support, rather than a rigid support, might be advantageous to improving the performance of an NSD. This study further simplifies the design of an NSD for multimode cable vibration control by leveraging the potential advantages of a flexible support. First, an equivalent model is established for the NSD support system. The deformation across the support is illustrated. Through parametric analysis, the parameter ranges for which the support flexibility exhibits various types of impacts on the damping force are obtained. Thereafter, to ensure rigidity, the lower limit of the support stiffness is determined. An optimization procedure is proposed for the single-mode cable vibration. The method of determination of the optimized NSD and its corresponding support is presented. On this basis, a simplified method is eventually developed for multimode cable vibration. A full-scale cable on a real bridge is adopted as the design prototype. A series of performance evaluations is conducted for validation. The theoretical and numerical results indicate that a small-sized NSD with a flexible support is capable of realizing the required damping. An optimized support stiffness is found to be independent of the vibration mode. Therefore, it may be concluded that only the highest mode should be taken into consideration and it considerably simplifies the design of the NSD for multimode cable vibration.