Archive of Applied Mechanics

, Volume 86, Issue 3, pp 557–573 | Cite as

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

  • Nguyen Van Khang
  • Axel Seils
  • Tran Ngoc An
  • Nguyen Phong Dien
  • Nguyen Trong Nghia
Original
  • 147 Downloads

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.

Keywords

Flutter instability Passive control Step-by-step analysis Numerical simulation Optimization Experimental study 

List of symbols

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Nguyen Van Khang
    • 1
  • Axel Seils
    • 2
  • Tran Ngoc An
    • 3
  • Nguyen Phong Dien
    • 1
  • Nguyen Trong Nghia
    • 4
  1. 1.Department of Applied MechanicsHanoi University of Science and TechnologyHanoiVietnam
  2. 2.Hamburg-Harburg University of TechnologyHamburgGermany
  3. 3.Vietnam Maritime UniversityHaiphongVietnam
  4. 4.Hanoi University of TransportHanoiVietnam

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