Table 5 Optimal characteristics of the TMDs according to different authors, where μ is the mass ratio between the mass of the TMD (m) and the structure (M), α is the frequency ratio between the TMD (ω) and the structure (ωs): and c and ξ are respectively the damping, and damping ratio of the TMD
From: Attenuation of pedestrian-induced vibrations in girder footbridges using tuned-mass dampers
Author | Frequency ratio α = ω/ωs | Damping ratio ξ = c /(2mω) |
|---|---|---|
Soong and Dargush (1997) | \( {\alpha}_{opt}=\frac{1}{1+\mu } \) | \( {\xi}_{opt}=\sqrt{\frac{3}{8}\frac{\mu }{{\left(1+\mu \right)}^3}} \) |
Warburton (1982) | \( {\alpha}_{opt}=\frac{\sqrt{1+\frac{\mu }{2}}}{1+\mu } \) | \( {\xi}_{opt}=\sqrt{\frac{\mu \left(1+\frac{3\mu }{4}\right)}{4\left(1+\mu \right)\left(1+\frac{\mu }{2}\right)}} \) |
Krenk et al. (2005) | \( {\alpha}_{opt}=\frac{1}{1+\mu } \) | \( {\xi}_{opt}=\sqrt{\frac{1}{2}\frac{\mu }{\left(1+\mu \right)}} \) |
Nishihara and Asami (2002) | \( {\alpha}_{opt}=\sqrt{\frac{1}{1+\mu }} \) | \( {\xi}_{opt}=\sqrt{\frac{3\mu }{8\left(1+\mu \right)}}\sqrt{1+\frac{27\mu }{32}} \) |