Closed-form optimal design of passive switching dampers for stay cables

Near-anchor linear viscous dampers for stay cables are constrained by the small local motion available for energy dissipation. This study proposes a passive switching damper that mechanically alternates between high- and low-damping states according to motion direction, without sensors, controllers, or external power. A first-harmonic reduction separates the non-smooth switching force into equivalent viscous and displacement-related components. Combined with complex-eigenvalue analysis, this representation yields the first-harmonic equivalent added modal damping ratio and a closed-form optimum for the high-state damping coefficient at a prescribed near-anchor location, while recovering the classical linear viscous damper (LVD) limit when the two damping states coincide. A detailed A10 stay-cable model is used to assess the analytical design against the fixed classical target-mode LVD under free decay, primary resonance, multi-frequency excitation, and stochastic aerodynamic loading. Without parameter retuning, the proposed damper reduces the maximum full-cable peak-displacement envelope by 26.67% under the prescribed three-frequency excitation. Across ten stochastic realizations, it reduces the mean mid-span RMS response by 31.40% relative to the LVD. Component tests at five excitation frequencies demonstrate passive two-state switching. A globally calibrated two-state force model achieves a mean normalized root-mean-square error (NRMSE) of 5.5%, compared with 14.6% for the linear viscous baseline. These component tests characterize local switching and force behavior rather than full-scale cable performance.