Coupled vibration control with tuned mass damper for long-span bridges

Long-span bridges undergoing wind excitation exhibit complex dynamic behaviors. Buffeting vibrations induced by wind turbulence happen throughout the full range of wind speed. As the wind speed increases, aerodynamic instabilities such as flutter may occur at high wind speed [1]. Much research effort has been made in mitigating excessive buffeting vibrations and improving aerodynamic stabilities for long-span bridges during construction [2,3] and at service [4–6]. Among all of the control procedures, dynamic energy absorbers such as tuned mass dampers (TMDs) have been studied in suppressing the excessive dynamic buffeting [7] or enhancing the flutter stability of bridges [4,8]. As traditional control devices, the dynamic energy absorbers dissipate external energy through providing supplemental damping to the modes of concern [9–11]. In a conventional TMD control design, the TMD frequency is designed or tuned to the modal frequency of the fundamental mode [12] in order to reduce the so-called resonant vibration and this method is thus called resonant-suppression approach here. When the modal coupling among the modes is weak, the bridge can be regarded as a simple combination of many single degree-offreedom (d.o.f.) systems and single mode analysis is usually applicable [13]. It is well-known that wind-induced aeroelastic effects result in additional aerodynamic damping and stiffness for long-span bridges [14]. The TMD control efficiency decreases with the increase of modal damping ratio. This implies that, for coupled mode vibrations of long-span bridges, the control efficiency of buffeting response of bending mode decreases with the increase of wind velocity since the aerodynamic damping of bending modes usually increases with the wind speed. Since bending modes usually contribute significantly to the overall buffeting response among all of the modes, the decreased control efficiency in bending modes may deteriorate the overall control efficiency of the bridge vibration. ARTICLE IN PRESS