Negative stiffness characteristics of active and semi-active control systems for stay cables

This paper examines the characteristics and effects of negative stiffness with active and semi-active control of stay cables for vibration reduction. The characteristics of negative stiffness of stay cable active and semi-active control are presented through numerical simulations. Three indices are defined to quantify the degree of negative stiffness. A pseudo-viscoelastic (P-VE) damper is proposed to replace an active or semi-active device to carry out numerical and theoretical analysis. An asymptotic solution of damping ratio of the combined cable/P-VE damper is obtained and the approximate optimal damping ratio of the combined cable/P-VE damper is further derived. The relationship between optimal damping ratio and the damping coefficient of the P-VE damper with various stiffness (both of negative and positive stiffness) is calculated by using the asymptotic solution and compared with that evaluated by using numerical analysis. The effect of negative stiffness on response reduction of cables is demonstrated by the improved energy dissipation ability of the damper and the increased approximate damping ratio because of the enhanced displacement of the cable at the location where it is attached to the damper.