Date of Award


Publication Type

Doctoral Thesis

Degree Name



Civil and Environmental Engineering

First Advisor

Shaohong Cheng

Second Advisor

Faouzi Ghrib


Cable-stayed bridge, NSD, Passive damper, Stay cable, Structural dynamics, Vibration control




Stay cables are one of the main structural elements in a cable-stayed bridge. Due to their high lateral flexibility and low inherent damping, cables are susceptible to large-amplitude vibrations that can adversely affect bridge safety and serviceability. As a practical measure, passive viscous dampers are installed transversely near the cable-deck anchorage. However, such devices can only provide a limited amount of damping. In recent years, the need for an effective yet simple control technique has led to the development of high-performance passive negative stiffness dampers (NSD). The present dissertation aims to study the behaviour of NSDs, enable their design for mitigating excessive bridge stay cable vibrations and evaluate their control effectiveness in comparison with other alternative schemes. To investigate the behaviour of NSDs, an analytical study has been conducted to obtain the in-plane free-vibration response of a shallow-flexural damped cable. The effect of damper stiffness was modeled as a linear spring aligned in parallel with a linear viscous dashpot. As a refinement to the existing damper design formulas, a unified design equation has been developed for the idealized fixed-fixed and hinged-hinged cable boundary conditions. The design procedure is based on an asymptotic solution to the modal damping ratio of the cable-damper system. The mode superposition method (MSM) has been adopted to numerically simulate the dynamic response of a controlled shallow-flexural cable subjected to arbitrary dynamic excitations. The numerical efficiency of the MSM was improved by including the cable static displacement caused by an arbitrary point load at the damper location as a correction term in the shape function vector and modifying the conventional sinusoidal shape functions to satisfy the boundary conditions. Results showed that the refined design formula yielded a slightly conservative estimation and therefore safe damper design. Also, the enhanced MSM-based numerical framework was found to substantially reduce the computational cost for designing cable vibration control schemes. Using the aforementioned analytical and numerical tools, the control performance of a NSD has been evaluated. The superior control effectiveness of a NSD compared to the positive- and zero-stiffness dampers was justified by employing the force generation mechanism of a viscous damper with linear stiffness. Theoretical and practical limits of the negative damper stiffness have been identified to ensure the stability of NSD and avoid unsafe design. An innovative NSD design procedure for mitigating both the single-mode and the multi-mode stay cable vibrations has been proposed. Analytical design relationships have been developed to determine NSD parameters for achieving the desired damping ratio in target mode(s). The impact of damper support flexibility on the NSD control performance has been studied to determine the optimum combination of NSD parameters and damper support stiffness. Results showed that the performance of a NSD designed/optimized based on the proposed methods was comparable to that of an optimal active controller. Furthermore, it has been found that optimizing NSD for a flexible damper support would result in a cost-efficient NSD design and inhibit additional NSD-induced cable displacement. The outcomes yielded from this dissertation extend the current knowledge associated with the dynamic behaviour of NSD-equipped bridge stay cables. The developed analytical/numerical tools and optimization methods contribute to the bridge industry by enabling accurate, efficient and reliable design of cable-NSD systems either in the preliminary design stage or during the rehabilitation process of cable-stayed bridges. The findings of this study will assist infrastructure management and improve the global economy by extending the life-span of cable-stayed bridges.