Impact of support stiffness on the performance of negative stiffness dampers for vibration control of stay cables

Abstract

Bridge stay cables are susceptible to dynamic excitations due to their low intrinsic damping and lateral stiffness. Installation of transverse passive dampers near the cable-deck anchorage on a rigid/flexible support is one of the practical measures to mitigate cable vibrations. The limited performance of conventional positive stiffness dampers (PSDs) has led to the emergence of negative stiffness dampers (NSDs). Recent research has found that unlike PSD, NSD would perform more effectively in the presence of a flexible support. In this study, the impact of damper support stiffness on the NSD control performance is investigated. Based on an existing analytical design formula for achieving a target damping ratio, the design of NSD for a given support condition, the design of damper support for a given NSD, and the design of the entire NSD-support system are addressed. An optimization algorithm is proposed to identify the optimum combination of NSD parameters and damper support stiffness. The NSD design is refined through numerical iterations to minimize the impact of assumptions made in developing the analytical formulation. A numerical example is presented for a 325 m long stay cable equipped with an optimized NSD and subjected to harmonic excitation. The optimized NSD performance is compared with an optimal active linear-quadratic regulator (LQR) controller. Results show that the presence of flexible support leads to a cost-efficient NSD with smaller size and lower level of negative stiffness. Moreover, the optimized NSD is shown to be as effective as LQR to suppress cable vibrations.