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An improvement of the step-by-step analysis method for study on passive flutter control of a bridge deck

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Abstract

The present study investigated the problem of increasing the critical flutter wind speed of long-span bridges by using tuned mass dampers (TMDs) on both theoretical and experimental aspect. The governing equations of motion of a bridge deck with TMD are analytically formulated. The method of step-by-step flutter analysis is improved and extended from the 2-DOF model to the 4-DOF model to calculate the critical flutter wind speed and parameters of TMD. A sectional model wind tunnel test is carried out to examine and validate the numerical results, and some new findings from the obtained results are included.

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Abbreviations

h :

Heaving motion

\(\alpha \) :

Torsional motion

\(\rho \) :

Air density

\(y_1 , y_2 \) :

Relative motion of TMD masses

B :

Deck width or along-wind dimension of the structure

l :

Longitudinal length of the test model

\(b_C \) :

Horizontal distance from TMD mass to the bending center of the test model

\(k_h , k_\alpha \) :

Stiffness associated with heaving motion and torsional motion, respectively

\(c_h , c_\alpha \) :

Damping coefficient associated with heaving motion and torsional motion, respectively

\(k_{_{C}} , c_{_{C}}\) :

Stiffness and damping coefficient of TMD, respectively

m :

Mass

I :

Mass inertia moment

\(m_C \) :

Mass of TMD

t :

Time

U :

Uniform approach velocity of the wind

\(U_F \) :

Critical flutter wind speed

\(U_{F\mathrm{opt}} \) :

Critical flutter wind speed with optimal flutter control

\(L_h , M_\alpha \) :

Self-controlled lift and moment, respectively

\(\omega \) :

Angular frequency of vibration

\(\omega _h , \omega _\alpha \) :

Angular natural frequency of heaving motion and torsional motion, respectively

\(f_C \) :

Natural frequency of TMD

\(\zeta _h , \zeta _\alpha \) :

Lehr damping corresponding to heaving motion and torsional motion, respectively

K :

Reduced frequency

\(H_i^*,A_i^*\) :

Flutter derivatives

\(\zeta _F \) :

Flutter Lehr damping

\(\omega _F \) :

Flutter angular frequency

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Acknowledgments

This paper was completed with the financial support of the Vietnam National Foundation for Science and Technology Development (NAFOSTED) and the German Research Foundation (DFG).

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Authors and Affiliations

  1. Department of Applied Mechanics, Hanoi University of Science and Technology, 1. Dai Co Viet Road, Hanoi, Vietnam

    Nguyen Van Khang & Nguyen Phong Dien

  2. Hamburg-Harburg University of Technology, Hamburg, Germany

    Axel Seils

  3. Vietnam Maritime University, Haiphong, Vietnam

    Tran Ngoc An

  4. Hanoi University of Transport, Hanoi, Vietnam

    Nguyen Trong Nghia

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  1. Nguyen Van Khang
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  2. Axel Seils
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  3. Tran Ngoc An
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  4. Nguyen Phong Dien
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  5. Nguyen Trong Nghia
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Correspondence to Nguyen Van Khang.

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Van Khang, N., Seils, A., An, T.N. et al. An improvement of the step-by-step analysis method for study on passive flutter control of a bridge deck. Arch Appl Mech 86, 557–573 (2016). https://doi.org/10.1007/s00419-015-1046-z

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