Abstract
Slender steel footbridges suffer excessive human-induced vibrations due to their low damping nature and their frequency being located in the range of human-induced excitations. Tuned mass dampers (TMDs) are usually used to solve the serviceability problem of footbridges. A multiple TMD (MTMD) system, which consists of several TMDs with different frequencies, has a wide application in the vibration control of footbridges. An MTMD system with well-designed parameters will have a satisfactory effect for vibration control. This study firstly discusses the relationship between the acceleration dynamic amplification factor and important parameters of an MTMD system, i.e., the frequency bandwidth, TMD damping ratio, central frequency ratio, mass ratio and the number of TMDs. Then, the frequency bandwidth and damping ratio optimal formulas are proposed according to the parametric study. At last, an in-service slender footbridge is proposed as a case study. The footbridge is analyzed through a finite element model and an in situ test, and then, an MTMD system is designed based on the proposed optimal design formulas. The vibration control effect of the MTMD system is verified through a series of in situ comparison tests. Results show that under walking, running and jumping excitations with different frequency, the MTMD system always has an excellent vibration control effect. Under a crowd-induced excitation with the resonance frequency, the footbridge with an MTMD system can meet the acceleration limit requirement. It is also found that the analysis result agrees well with the in situ test.
Highlights
Because of the beautiful architectural appearance, short construction period and high economy, slender steel footbridges became more and more popular than before and were common in urban areas [1,2,3,4,5,6,7,8]
One of the most traditional structural control devices was the tuned mass damper (TMD), which consisted of a mass element, a stiffness element and a damping element
Tubino and Piccardo [23] optimized a TMD to control the human-induced vibration of footbridges
Summary
Because of the beautiful architectural appearance, short construction period and high economy, slender steel footbridges became more and more popular than before and were common in urban areas [1,2,3,4,5,6,7,8]. Considering that the damping ratio of the slender footbridge is low and for simplification, in the following parametric discussion, ξs is ignored and set to be zero It can be known from Reference [23] that for a single TMD, the optimal frequency is fT = 1/(μ + 1), and it is reasonable when fT = 1. To find a better choice for the MTMD system, these two cases will be compared in the following
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