Due to their high lateral flexibility and low inherent damping, stay cables are prone to dynamic excitations. Application of dampers to improve the energy dissipation capacity of stay cables and mitigate their excessive vibrations has been extensively studied, and design tools have been proposed to select the optimum damper size and predict the maximum achievable damping ratio of a cable-damper system. In this study, the effectiveness of external viscous dampers in controlling stay cable vibrations is investigated by considering the negative stiffness behavior of passive dampers. An analytical model is developed to include the damper stiffness effect for further refinement of existing damper design tools, of which the influence of cable sag, cable flexural stiffness, and damper support stiffness has already been considered. The performance of passive negative stiffness dampers (NSDs) and conventional zero or positive stiffness dampers (PSDs) is investigated in detail via parametric studies using the refined design formula. In particular, a criterion is defined for selecting the negative stiffness in NSD based on the stability limits. Two design examples are presented to illustrate the application of the proposed refined damper design tool to the selection of optimum damper size and evaluation of damper performance for a passive viscous PSD and NSD. Results show that compared with the conventional viscous dampers, a passive NSD demonstrates superior performance in stay cable vibration control. Results are also compared and verified with the numerical solution of the proposed analytical model.

Summary Due to their low inherent damping and high lateral flexibility, stay cables are prone to large amplitude vibrations governed by either a single or multiple cable modes. Among the practical measures, the installation of transverse passive dampers near the cable‐deck anchorage is a popular choice. Compared to conventional positive stiffness and zero stiffness dampers, negative stiffness damper (NSD) manifests superior performance in mitigating cable vibrations, especially in the case of long cables. In this study, a novel design approach is proposed to optimize NSD for multimode cable vibration control. Two design scenarios are considered. In the former, the damper size is optimized for a predetermined negative damper stiffness; whereas in the latter, the size and negative stiffness of the NSD are both optimized to achieve a required damping ratio for the dominant modes. The applicability of the proposed NSD optimum design approach is validated using 15 sample real stay cables. A numerical example is presented, of which a NSD is designed based on the proposed approach to optimize wind‐induced multimode vibration control of a 460‐m stay cable, and the performance is compared with that of a linear‐quadratic regulator (LQR) control. Results show that the selected NSD can effectively suppress the dominant modes and has a controlling effect comparable with an active control using LQR. In addition, it is found that when there exist more than two dominant modes in vibration, designing NSD for the lowest and the highest dominant modes would also adequately control the mid‐range modes.

The idea of using semi-active or active control devices within a base isolation system has been developed recently, since applying this system to building structures has some shortcomings such as the creation of large displacements at the base level and the systemʼs lack of adaptability to different seismic excitations. In this study, an integrated structural health monitoring and semiactive control scheme is proposed to enhance the seismic behavior of damaged isolated structures. The nonlinear behavior of an isolated structure is limited to the isolator level and the superstructure is assumed to remain linear. Then, using an online damage detection algorithm based on identified system Markov parameters and a semi-active fuzzy controller, the damage in the base isolator is mitigated and the seismic response of the structure is reduced. In addition, a magnetorheological damper is utilized as a well-studied semi-active actuator in the control system. The effectiveness of the proposed control system is evaluated through the numerical study of a six-degrees-of-freedom model of base-isolated buildings excited by various near-fault and far-field earthquake records. The results of the simulation show that the integrated algorithm is substantially effective in improving the dynamic behavior of isolated structures and reducing the damage in the isolator.

Summary 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.

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