STRUCTURAL CONTROL AND HEALTH MONITORING Struct. Control Health Monit. 2011; 18:265–288 Published online 2 December 2009 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/stc.368 Seismic response control of a cable-stayed bridge using negative stiffness dampers Hui Li 1,Ã,y , Jinlong Liu 1 and Jinping Ou 1,2 1 School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China 2 School of Civil Engineering and Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China SUMMARY The seismic behavior of a cable-stayed bridge incorporated with negative stiffness dampers (may be active or semi-active dampers, simulated by pseudo-viscoelastic (P-VE) dampers) between the tower and deck is investigated. First, the relationship of bridge damping ratio and connection stiffness between the middle tower and deck is deduced from a simplified cable-stayed bridge model. The maximum damping ratio of the cable-stayed bridge occurs when the optimum connection stiffness is reached. It is found that the optimum connection stiffness is composed of two negative values, indicating that the damper stiffness should be taken to be negative. Furthermore, the nonlinear seismic behavior of the cable-stayed bridge with P-VE dampers is studied through the numerical simulations. The reduction in the seismic response of the cable-stayed bridge incorporated with the negative stiffness dampers is demonstrated. The influence of the stiffness of P-VE dampers on the seismic behavior of cable-stayed bridges is investigated. The results indicate that the seismic performance of the cable-stayed bridge is the best and the damping ratio of the bridge achieves its maximum value when the damper stiffness is optimum. The optimum stiffness for the bridge at nonlinear stage is identical to that at linear phase. Copyright r 2009 John Wiley & Sons, Ltd. Received 2 January 2009; Revised 9 July 2009; Accepted 26 October 2009 KEY WORDS: negative stiffness damper; cable-stayed bridge; optimum stiffness; seismic; structural control 1. INTRODUCTION Cable-stayed bridges are a type of long-span bridge, however, the dynamic oscillation of cable- stayed bridges may be dramatic due to their small inherent structural damping [1,2]. The reduction of dynamic response of cable-stayed bridges induced by the environmental and service dynamic loads is considered to be of vital importance for their safety and serviceability. In an earlier investigation of control of cable-stayed bridges, Ali and Ghaffar [3], Villaverde and Martin [4], Ingham et al. [5] studied the passive seismic control method of cable-stayed bridges with dampers; Yang and Giannopoulos [6], Warnitchai et al. [7], Achkire and Preumont [8], Schemmann and Smith [9,10], Iemura and Pradono [11] proposed the active or semi-active control technology to mitigate the dynamic response of cable-stayed bridges. The working group on bridge control within the ASCE Committee on structural control posed the first-generation benchmark structural control problem based on the Cape Girardeau Bridge and updated it to a second-generation benchmark model [12–14]. Benchmark structural *Correspondence to: Hui Li, School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China. y E-mail: lihui@hit.edu.cn Contract/grant sponsor: Ministry of Science and Technology; contract/grant number: 2007CB714204, 2007CB714205, 2006BAJ03B06 Copyright r 2009 John Wiley & Sons, Ltd.