## 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. Tiff | Fig. 1. Bridge deck with eccentric-wing flutter stabilizer – cross section. | |

Fig. 2. Tiff | Fig. 2. Non-dimensional flutter speed, , of undamped system without wings against frequency ratio, ζε. | |

JPG | Fig. 3. Tiff | Fig. 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. |

JPG | Fig. 4. Tiff | Fig. 4. Ratio of flutter speed of damped system (= 0.01) to flutter speed of undamped system, both without wings, against frequency ratio, gε. |

JPG | Fig. 5. Tiff | Fig. 5. Flutter speed increase ratio, R, for undamped system, wing mass neglected, against frequency ratio, ε (ã_{c} = 2.0, b _{c} = 0.1, L_{c }= 1). |

JPG | Fig. 6. Tiff | Fig. 6. Flutter speed increase ratio, R, for damped system, wing mass considered, against frequency ratio, ε (g = 0.01, ã_{c} = 2.0, b_{c} = 0.1, L_{c }= 1, m_{c }= 0.015). |

JPG | Fig. 7. Tiff | Fig. 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 (ã_{c }= 2.0, b_{c} = 0.1, L_{c} = 1, mc = 0.015). |

JPG | Fig. 8. Tiff | Fig. 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 (ã_{c }= 2.0, b_{c} = 0.1, L_{c} = 1, m_{c}= 0.015). |

JPG | Fig.9. Tiff | Fig. 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, ã_{c} = 2.0, b_{c} = 0.1, L_{c =} 1, m_{c} = 0.015). |

JPG | Fig.10. Tiff | Fig. 10. Flutter speed increase ratio, R, for damped system, wing mass considered, against relative wing eccentricity, ã_{c }(r = 0.8, g = 0.01, b_{c} = 0.1, L_{c} = 1, m_{c} = 0.015). |

JPG | Fig. 11. Tiff | Fig. 11. Flutter speed increase ratio, R, for undamped system, wing mass neglected, against relative wing width, b_{c} (r = 0.8, ã_{c} = 2.0, L_{c} = 1). |

JPG | Fig. 12. Tiff | Fig. 12. Flutter speed increase ratio, R, for damped system, wing mass considered, against relative wing length, L_{c} (r = 0.8, g = 0.01, ã_{c} = 2.0, b_{c} = 0.1, m_{c }= 0.015). |

JPG | Fig. 13 . Tiff | Fig. 13. Torsional component of flutter mode shape for ε = 1.3, μ = 15, r = 0.8, g = 0.01, ã_{c }= 2.0, b_{c} = 0.1, L_{c} = 0.20, m_{c }= 0.015. |

JPG | Fig. 14. Tiff | Fig. 14. Torsional component of flutter mode shape for ε = 1.3, μ = 15, r = 0.8, g = 0.01, ã_{c} = 2.0, b_{c} = 0.1, L_{c}= 0.32, m_{c }= 0.015. |

JPG | Fig. 15. Tiff | Fig. 15. Complex eigenfrequencies against reduced wind speed, 1=k, for ε = 1.3, μ = 15, r = 0.8, = 0.01, gã_{c} = 2.0, b_{c }= 0.1, L_{c} = 0.20, m_{c} = 0.015. |

JPG | Fig. 16. Tiff | Fig. 16. Complex eigenfrequencies against reduced wind speed, 1=k, for ε = 1.3, μ = 15, r = 0.8, g = 0.01, ã_{c} = 2.0, b_{c }= 0.1, L_{c} = 0.32, m_{c }= 0.015. |