Parametric flutter analysis of bridges stabilized with eccentric wings

Starossek, U.; Starossek, R. T. (2021). "Parametric flutter analysis of bridges stabilized with eccentric wings." Journal of Wind Engineering & Industrial Aerodynamics, Vol. 211, April 2021. doi.org/10.1016/j.jweia.2021.104566. 

 

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Fig. 1. TiffFig. 1. Bridge deck with eccentric-wing flutter stabilizer – cross section.
Fig. 2. TiffFig. 2. Non-dimensional flutter speed, ζ, of undamped system without wings against frequency ratio, ε.
Fig. 3. TiffFig. 3. Non-dimensional flutter speed, ζ, against frequency ratio, ε, for various conditions: A = no wings, undamped, B = no wings, damped, C = with wings, undamped, wing mass neglected, D = with wings, undamped, wing mass considered, and E = with wings, damped, wing mass considered.
Fig. 4. TiffFig. 4. Ratio of flutter speed of damped system (g= 0.01) to flutter speed of undamped system, both without wings, against frequency ratio, ε.
Fig. 5. TiffFig. 5. Flutter speed increase ratio, R, for undamped system, wing mass neglected, against frequency ratio, ε (ãc = 2.0, b c = 0.1, Lc = 1).
Fig. 6. TiffFig. 6. Flutter speed increase ratio, R, for damped system, wing mass considered, against frequency ratio, ε (g = 0.01, ãc = 2.0, bc = 0.1, Lc = 1, mc = 0.015).
Fig. 7. TiffFig. 7. Flutter speed increase ratio when wing mass considered referred to flutter speed increase ratio when wing mass neglected, for undamped system, against frequency ratio, ε (ãc = 2.0, bc = 0.1, Lc = 1, mc = 0.015).
Fig. 8. TiffFig. 8. Flutter speed increase ratio for damped system (g – 0.01) referred to flutter speed increase ratio for undamped system, wing mass always considered, against frequency ratio, ε (ãc = 2.0, bc = 0.1, Lc = 1, mc= 0.015).
Fig.9. TiffFig. 9. Flutter speed increase ratio, R, and ratio of divergence speed to flutter speed without wings, against frequency ratio, ε (r = 0.8, g = 0.01, ãc = 2.0, bc = 0.1, Lc = 1, mc = 0.015).
Fig.10. TiffFig. 10. Flutter speed increase ratio, R, for damped system, wing mass considered, against relative wing eccentricity, ãc (r = 0.8, g = 0.01, bc = 0.1, Lc = 1, mc = 0.015).
Fig. 11. TiffFig. 11. Flutter speed increase ratio, R, for undamped system, wing mass neglected, against relative wing width, bc (r = 0.8, ãc = 2.0, Lc = 1).
Fig. 12. TiffFig. 12. Flutter speed increase ratio, R, for damped system, wing mass considered, against relative wing length, Lc (r = 0.8, g = 0.01, ãc = 2.0, bc = 0.1, mc = 0.015).
Fig. 13 . TiffFig. 13. Torsional component of flutter mode shape for ε = 1.3, μ = 15, r = 0.8, g = 0.01, ãc = 2.0, bc = 0.1, Lc = 0.20, mc = 0.015.
Fig. 14. TiffFig. 14. Torsional component of flutter mode shape for ε = 1.3, μ = 15, r = 0.8, g = 0.01, ãc = 2.0, bc = 0.1, Lc= 0.32, mc = 0.015.
Fig. 15. TiffFig. 15. Complex eigenfrequencies against reduced wind speed, 1=k, for ε = 1.3, μ = 15, r = 0.8, g = 0.01, ãc = 2.0, bc = 0.1, Lc = 0.20, mc = 0.015.
Fig.  16. TiffFig. 16. Complex eigenfrequencies against reduced wind speed, 1=k, for ε = 1.3, μ = 15, r = 0.8, g = 0.01, ãc = 2.0, bc = 0.1, Lc = 0.32, mc = 0.015.