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Suspension Bridge 

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1234567895. Suspension Bridge Flutter

Flutter Modal Force (no control)

Small displacements of the suspension bridge girder

(because of wind) interacting with the wind velocity

U result in the motion-induced forces that again can

produce violent vibration and develop into destructive

mode (flutter mode) within a short time, as mentioned

earlier in Chapter 1, [00,0]. The flutter mode can be a

combination of several modes, but is primarily in the

vertical and the torsional mode at the lowest

frequencies, where the critical frequency wcr is the

one between them.

The motion of one joint on the girder
can be
described by three translations and three rotational
components, which can be written in the deformation
vector v(x,t), Figure 5.1

k(x) is the undamped mode shape vector in mode k,
in which
fx,k , fy,k and fz,k are the longitudinal, lateral
and vertical translation component,
yx,k , yy,k , and
yz,are the rotational component about the x-, y-
and z-axis, respectively.
xk(t) is the corresponding
modal coordinate and ndof  is theoretically the total
number of degrees-of-freedom of all the joints created
in the bridge.

In (5.2) the physical displacement vz(x,t) in purely

vertical mode i and the physical rotation rx(x,t) in

purely torsional mode j can be written as independent

modal coordinates in the form (5.3) and (5.4), where

fi(x) and yj(x) are the vertical and torsional modes

that couple to produce flutter vibrations.


The modal force Fdeck(t) due to a coupled vertical-

torsional mode k is given by (5.5) which can be

written as the vertical modal equation Fz(t) and

torsional modal equation Fx(t).


The question of how many and what modes a

suspension bridge couples at the flutter mode (beyond

the SV1 and ST1) refers to a lot of factors depending

on each individual case. During the CAE work to

identify the natural modes, one can see that many of

the modes (in low frequency range) look like each other

with closed natural frequencies. Considering this

information, a number of important modes can be

selected for the multimode coupled flutter computation.

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Wind Loads on the Girder and on the control Flaps

The total motion-induced wind loads per unit span on
a girder cross-section including the leading and trailing
flaps are shown in Figure 5.2. The same coordinate
system and definition of the girder deformations as
Figure 5.1 is used, but the flaps and their deformation
directions are shown. The system is assumed to
oscillate from position B to C at wind action U.

It is assumed that the generalised forces caused by

the girder-wind-interaction and the generalised forces

caused by the flap-wind-interaction (for separate flaps)

are computed on the independent flutter derivatives of

the girder and of the flaps.


When the girder vibrates in the coupled vertical/

torsional mode, the generalised moment of the flaps is

composed of two contributions. One refers to the

“purely” vertical motion of the girder and the rotation

of the flaps (that computed from the rotation of the

girder). The other refers to the vertical motion of the

girder due to the girder rotation and the same rotation

of the flaps.


A new graphical solution for solving the flutter

conditions using Maple is introduced in [00,0].

There are no needs for a reduced frequency K and a

reduced wind velocity u in the between step, since

the critical frequency wcr and the critical wind

velocity Ucr can be solved directly. Moreover, the

change of any equation to produce the flutter

conditions (e.g. the flutter derivative functions)

can be estimated numerically. 

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6. Buffeting Response of Suspension Bridge Girder

    with and without Separate Control Flaps


Single-mode buffeting response is assumed in this

chapter for several reasons. Firstly, to be able to

reduce the complications related to the additional

control flaps. Secondly, it is easier to operate the

multimode coupled buffeting response from the single-

mode analysis (Section 7.4). Thirdly, since the buffeting

response occurs at a lower mean wind velocity than

flutter, the aerodynamic effects that cause modal

coupling will not produce significant differences between

the two assumptions (see e.g. [99,2]). Finally, to ensure

that the single-mode vibrations do not develop a

catastrophic vibration amplitude.


Expression (6.7) to (6.10) are the buffeting-induced lift

and moment per unit span of the deck, the leasing flap

(le) and the trailing flap (tr), respectively. u(x,t) is the

along wind turbulence component and w(x,t) is the

vertical turbulence component. CL , CM , and CD are the

non-dimensional lift and the moment and drag coefficient,



The mean wind velocity is assumed to be smaller at
buffeting conditions than at those causing coupled
instabilities. Thus, the uncoupled aeroelastic forces are
transferred to the left-hand side of the motion equation
to modify the natural frequency and the structural
damping ratio to the new quantities in the stochastic
buffeting modal equation, cf. [00,0].

You can download entire PhD Thesis in Reference below

12345678Alternative Text




Truc Huynh & Palle Thoft-Christensen, "Suspen­sion Bridge Flutter for Girder with Separate Control Flaps”, Journal of Bridge Engineering,
ASCE p.168-175, May/Jun 2001 Vol.6 No.3 or 
ISSN 1395-7953 R0013



Truc Huynh, "Suspension Bridge Aerodynamics and Active Vibration Control", PhD Thesis, Aalborg University Denmark,
ISSN 1395-7953 R0015

Truc Huynh & Palle Thoft-Christensen, "Buffeting Response of Suspen­sion Bridge Girder with Separate Control Flaps”,
Presented in Second European Conference on Structural Control, Paris July 2000, 
ISSN 1395-7953 R0014


Nielsen, S. R. K & Truc Huynh “Vibration Theory, Vol. 7A. Special Structures: Aerodynamics of Suspension Bridges,
Aalborg University Denmark, 
ISSN 1395-8232 U9902


Katsuchi H., N. P. Jones & R. H. Scanlan “Multimode Coupled Flutter and Buffeting Analysis of the Akashi-Kaikyo Bridge”,
Journal of Structural Engineering /January 1999, Vol. 125, No. 1

 1997[2] Dyrbye C. & S. O. Hansen, Wind Load on Structures, John Wiley & Sons. 
 1992[3]Scanlan R. H.  “Wind dynamic of long-span bridges”, Larsen A. editor [1992,1, pp. 47-57].

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