Robustness Evaluation of Negative Stiffness Damper for Cable Vibration Mitigation Based on Interval Model with Experimental Validation

The negative stiffness damper (NSD) has emerged as a promising passive vibration control device for cable structures due to its simplicity and effectiveness. However, uncertainties stemming from both internal and external environmental factors can potentially compromise the NSD's performance in real-world applications, posing risks to cable safety. In response, this paper conducts a robustness evaluation on an integrated cable-NSD system, taking into account various potential uncertainties. Specifically, the uncertain parameters are described by interval variables. Consequently, an interval model is constructed to delineate the boundaries of cable dynamic responses when subjected to these uncertainties. The model's accuracy is validated against experimental results. Subsequent simulations involve assessing interval responses for both single- and multimode cable vibrations under varying uncertainties. Finally, the NSD's robustness concerning cable vibration control is evaluated using the model, which incorporates the first-passage theory. This analysis delves into the relationships among confidence levels, performance measures, and the variation range of uncertainties. The results indicate that for single-mode vibration control, there is a 90% confidence level that the damping ratio reduction remains within 10%. As for multimode vibration control, a 90% confidence level is established that the amplification falls within 17%.