Optimal Design of Nonlinear Negative-Stiffness Damper with Flexible Support for Mitigating Cable Vibration

Abstract

Negative-stiffness damper is a promising device to mitigate cable vibrations effectively. In contrast to traditional rigid supports, recent study has found that flexible supports are actually beneficial for enhancing the performance of negative-stiffness dampers. This study extends the understanding of the impact of support flexibility under nonlinear condition, followed by an optimization process to obtain required negative-stiffness dampers and corresponding supports. First, taking damping nonlinearity into account, a unified model is established for the negative-stiffness damper with flexible support. Theoretical equivalent negative stiffness and damping are obtained for a linear case, followed by numerical verification. Thereafter, equivalent parameters under a friction case are presented. Experiments are conducted to validate the analytical derivation. Then, problem formulation is developed for the controlled cable. Optimization process is proposed to determine the required negative-stiffness damper and support for multimodal cable vibration. A series of numerical simulations are performed to demonstrate the design process. Moreover, nonlinear examples are presented to show the potential for improving control performance. As indicated by the research results, a flexible support is capable of amplifying the equivalent negative stiffness and damping under linear and nonlinear conditions. For multimodal cable vibration, it is sufficient to determine the optimized negative stiffness and support by only considering the highest mode. Nonlinear negative-stiffness dampers exhibit superior performance due to the leakage of vibration energy toward high-order modes.