DRY GALLOPING CHARACTERISTICS AND ITS MECHANISM …bbaa6.mecc.polimi.it/uploads/validati/cce03.pdf · 1 BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications

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BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications

Milano, Italy, July, 20-24 2008

DRY GALLOPING CHARACTERISTICS AND ITS MECHANISM OF INCLINED/YAWED CABLES

Masaru Matsumoto∗, Tomomi Yagi∗, Hideaki Hatsuda†, Takanori Shima‡, Masanobu Tanaka# and Hiroko Naito∗

∗ Department of Civil and Earth Resources Engineering, Kyoto University Kyotodaigaku-katsura, Nishikyo-ku, Kyoto 615-8540, Japan

e-mail: [email protected] † Tokuyama Corporation, Shibuya Konno Bldg. 3-3-1, Shibuya Shibuya-ku, Tokyo 150-8383, Japan

‡ IHI Corporation, Toyosu IHI Bldg., 1-1, Toyosu 3-chome, Koto-ku, Tokyo 135-8710, Japan(2008.4~)

# Penta Ocean Construction Co., Ltd., 2-8 Koraku 2-chome, Bunkyo-ku, Tokyo 112-8576, Japan(2008.4~)

Keywords: inclined-cable-aerodynamics, dry-galloping, role of Karman vortex, quasi-steady galloping, unsteady galloping

1 Introduction The complicated inclined cable aerodynamics has being clarified through a lot of wind

tunnel tests and researches. As a state of art of inclined cable aerodynamics, it can be under-stood that rain vibration (RV) is caused by formation of upper water rivulet at particular posi-tion on cable-surface and axial flow, which flows along cable-axis, in near wake of cable [1, 2, 3]. On the other hand, as far as dry galloping, the axial flow and critical Reynolds number, Recr., play definitely important role for the excitation [4, 5]. Recently, authors have discussed these cable aerodynamic vibrations in relation to Karman vortex shedding. For RV, both of upper water rivulet and the axial flow can mitigate KV and sequentially RV, which is like gal-loping instability, can be excited. For DG, both of critical Reynolds number and the axial flow can also individually mitigate KV.

Sometimes, significantly sever cable vibration have been observed in the field for proto-type cable-stayed bridges. How to stabilize these cable vibrations is one of the most important safe design factors for bridges. The damping devises to increase structural damping [6, 7] or modification of cable geometrical shape have been so far used to control the cable vibration [8, 9]. Recently in U.S. to achieve this matter, three different countermeasures are simultaneously used [10]. Those are cables lapped by PE with helical fin on cable surface, cross ties between stay-cables and damping devices. In particular, how to determine the damping capacity to suf-ficiently suppress DG is the most concerned. Then, FHWA in U.S. [10] proposed the original diagram on Vrcr.- Scruton number, Sc, so called as FHWA criterion as shown in Fig.1 to de-termine the required damping capacity for practical use. However, Saito [8] formally reported different wind tunnel test results associated to Sc-Vrcr. Diagram (see Fig.1), so called Saito

M. Matsumoto, T. Yagi, T. Shima, M. Tanaka, H. Naito and H. Hatsuda

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criterion. As shown, there is great difference between two criteria, in another expression, bas-ing on Saito criterion, it is really difficult to suppress DG by increasing structural damping. The clarification of definite discrepancy between two criteria is one of the most important is-sues in nowadays bridge aerodynamics. If using recent finding by one of author on galloping instability of bluff body aerodynamics in relation with KV role, the key to resolve this prob-lem is found. Furthermore, galloping can be classified into two different types, those are un-steady galloping and divergent type quasi-steady galloping, depending on the controlled KV characteristics of bluff bodies [9].

On the other hand, the mechanism of galloping of bluff bodies has been studied by Naka-mura [11], and he concluded that the interruption of “communication” between two separated shear layers in near wake can produce the reattachment-type of pressure distribution and it can excite galloping instability.

In this paper, the DG of inclined cables being targeted, how to control DG and considera-tion on the mechanism of DG are studied basing on a series of wind tunnel tests.

2 Field observation of DG for proto-type cable stayed bridge [1] The wind-induced vibration of inclined cables of cable stayed-bridges have been mostly

observed under the state of precipitation, that is well known as rain-wind induced vibration, however, the wind tunnel tests have reported the galloping instability of inclined/yawed cable at the dry state, it means without rain. Recently, in Japan, an inclined PE-lapped cable with 187m length of certain cable-stayed bridge showed the violent vibration, during passing of Typhoon, whose amplitude was estimated than 1.5m, and this vibration severely damaged not only a part of edge faring installed to aerodynamically stabilize at bridge girder edges but also cable surface, as shown in Fig.2.

The estimated wind velocity was approximately 18m/s and wind blew with some yawing angle to bridge axis, which were not precisely measured on the bridge site but based upon the

Figure 1: Comparison of wind velocity-damping relation of inclined dry cable

Saito Instability Line Saito θ=45°, β=0° Miyata FHWA Small Amplitude <10mm FHWA 10mm to 80mm Amplitude FHWA Maximum Amplitude 80mm FHWA Instability Line

Figure 2: Violent cable vibration observed at certain proto-type cable-stayed bridge in Japan (courtesy of Mr. H. Yoshikawa)


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data measured at a meteorological observatory located at approximately 1km upstream side from bridge, and some eyewitness reported that rain had already stopped when cable violently vibration started. The viscous damper had been installed at the cable-end on the ground, be-cause of curved bridge-girder, but it was completely destroyed after a violent cable vibration, however it was not cleared whether this damper was damaged before or after the violent cable vibration. Therefore, this vibration might be a dry-state galloping, even though less detail data at the bridge site on that day.

3 Axial flow effect on inclined cable aerodynamics Ones of authors have pointed out the important role of axial flow in a wake of in-

clined/yawed cable without rivulet, in another expression at the dry-state, for galloping insta-bility [12]. Axial flow velocity in near wake has been measured by use of hot-wire anemometer for yawed rigid cable model in wind tunnel and it be cleared that the axial flow velocity increased with yawing angle, β, to approaching wind. Furthermore, this velocity dis-tributes non-uniformly along cable axis from the upstream cable end to the downstream one. Three cable-end conditions were tested, such as (1) free cable ends and without tunnel-walls, (2) with end-plates and without tunnel-walls and (3) with tunnel-walls installed suitable holes, so called “window”, at cable ends. In order to survey the effect of cable end condition on ax-ial flow velocity, the axial flow velocity was measured in a wake for three different cable end cases. The intensity of those particular flow velocities is not so different in three cable end cases, exception at near upstream cable end, as shown in Fig.3 (V=8m/s, β=45º, in smooth flow). At near the upstream cable end, the axial flow velocity is almost 80% for the end con-dition case (3), 70% for the case (1) and 50% for the case (2) of approaching wind velocity, respectively, however, at the downstream side from the quarter point of cable length, its inten-

Figure 3: Axial flow velocity (Va) in a wake of yawed cable model (V=8m/s, β=45˚, in smooth flow)

wind

X

: (1) without wall : (2) without wall and with end plates: (3) With walls installed windows 0 200 400 600 800 1000 1200

0

2

4

6

8

X [mm]

Va

(m/s)

Figure 4: visualized axial flow by light strings for a proto-type cable

wind


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sity is 60% to 40% with the trend of gradually decreasing to the downstream end for all three end conditions. On the other hand, the axial flow was visualized in the field by use of light strings for the proto-type inclined cable with vertical angle (α) of 30, which corresponds to equivalent yawing angle [13], β* of 40º~50º, from the point of relative cable attitude to wind, as shown in Fig.4 and its velocity was measured by a soap-bubble movement in a wake taken by video camera. Measured axial flow velocity distributed between 40% and 80% to ap-proaching wind velocity, as shown in Fig.5, which corresponds well to wind tunnel test re-sults explained before.

The artificial axial flow, generated by compressor and electrical cleaner as shown in Fig.6 can reproduce significantly similar galloping instability, which onsets at the particular re-duced velocity of Vr=V/fD=40 similarly with one of yawed cable model with β=45º, for non-yawed (β=0º) cable model [14] (see Fig.7). This test result indicates clearly the axial flow in near wake can excite galloping. Taking account the similar role of axial flow with a splitter plate installed in near wake, the axial flow must interrupt KV shedding in near wake. How-ever, V-A diagram of cross-flow response indicated different characteristics as indicated in Fig.8, because the intensity of axial flow changes along yawed-cable (β=45º) axis, depending on the cable end-conditions, including with free end, with end-plates and with suitable-size window on wind-tunnel wall.

0 2 4 6 80

2

4

6

8

Mean wind velocity [m/s]

Va

(m/s

)

Figure 5: Axial flow velocity and approaching wind velocity of a stay-cable (β*=40°-50°, where β*: equivalent yawing angle [13])

Figure 6: Article axial flow generator Figure 7: Galloping appearance for non-yawed/inclined cable with artificial axial flow


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4 Critical Reynolds number effect on Inclined cable aerodynamics Schewe [15] pointed out that drag force is remarkably reduced, stationary lift force can be

generated and KV shedding is significantly suppressed for circular cylinder at Critical Rey-nolds number. Furthermore, Cheng et al. [16] found inclined (β=0º and α=45º) cable model also produces stationary lift force with significant drag reduction at Critical Reynolds number. Macdonald [17] successfully realized the galloping instability by use of quasi-steady analysis basing on test result obtained by Cheng. On the other hand, the authors verified the critical Reynolds number effect by use of yawed cable model with artificial roughness on galloping instability. It means the stationary lift and significant drag reduction and KV suppression at critical Reynolds number as shown in Fig.9. The cross flow response is not divergent type galloping but unsteady response can be observed at Critical Reynolds number as shown in Fig.10. Furthermore, basing on Scanlan derivative H1

* in terms of heaving velocity, it shows positive value, unstable state for galloping, at critical Reynolds number by realized by particu-lar combination of velocity and forced vibration frequency as shown in Fig.11.

(1) without wall

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V/fD

f=2.87Hzm=0.680kg/mδ(2A=10mm)=0.0032Sc(2A=10mm)=1.43

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wind

Walls without/with windows

Figure 8: Velocity - Amplitude diagrams in various cable-end conditions (β=45°, D=50mm, in smooth flow)

0 0.5 1 1.5 2-0.4-0.2

00.20.40.60.8

11.2

Reynolds Number (x105)

Var

ious

win

d fo

rce

coef

ficie

nts

Wind Velocity (m/s)0 3 6 9 12 15 18

Figure 9: Wind force coefficients for a cable model with surface roughness (β=0º, D=158mm, in smooth flow)

Lift coefficient CL Drag coefficient CD Fluctuating lift coefficient


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5 FHWA Criterion and Saito Criterion associated Scruton number and galloping on-set reduced velocity characteristics

As described above, recently FHWA proposed a new criterion on Scruton number and gal-loping onset reduced velocity characteristics for DG [10] for practical use for bridge designers. However, there are significant difference at large Scruton number between FHWA Criterion and the characteristics formally reported by Saito as shown in Fig.1. As shown, basing on Saito criterion, it is really difficult to suppress DG by increasing structural damping. Tough the amplitude of unsteady galloping fitted by Saito’s criterion at large Scruton number is not so large, therefore from the practical point of view, unsteady galloping might not directly in-terfere the safety of inclined cables, however, the clarification of definite discrepancy between two criteria must be one of the important issues in bluff body aerodynamics.

6 Similarity between RV and DG For RV, extremely important role of formation of upper water rivulet at particular position

on yawed/inclined cable surface for aerodynamic excitation has been understood. As shown in Fig.12, galloping appears if KV is significantly suppressed by water rivulet formation at par-ticular position for both of non-yawed cable and yawed (β=45º) cable. In consequence, there are significant similarity between RV and DG from points of galloping appearance in relation with suppression of KV. However, taking into account of movement and non-uniform-distribution of upper water rivulet during cable vibration as shown in Fig.13, therefore gallop-ing with large amplitude can be hardly excited due to formation of upper water rivulet, as al-ternatively mostly beat vibration like snake dance has been mostly observed in the field. In

Figure 11: Aerodynamic derivative H1* with surface roughness

(β=0°, 2η=10mm, D=158mm, in smooth flow)

-80

-40

0

40

80

0 30 60 90 120 150 180 210

U/fD

H1*

Re=47000 Re=62000 Re=93000 Re=166000

-320

-160

0

160

320

0 30 60 90 120 150 180 210

U/fD

H1*

Re=109000 Re=120000 Re=130000 Re=135000 Re=140000

Figure 10: Velocity - Amplitude diagrams (β=0º, D=158mmsurface-roughnes, in smooth flow)

0 2 4 6 8 10 12 14 16 18 0

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40

60

80

2A/D 2A [mm]

U [m/s]U/fD

Re(x105)


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(a) β=0°

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U [m/s]U/fD

f=1.73Hzm=0.82kg/mδ (2A=10mm)=0.0038Sc (2A=10mm)=2.05

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P.S.

D. [

(N/m

)2 /Hz]

P.S.D. of the fluctuating lift force on stationary cable model (U=6.0m/s)

Figure 12: Rivulet position effect on Velocity - Amplitude diagrams of non-yawed, yawed cable model (D=54mm, in smooth flow)

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U [m/s]U/fD


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θ=66°

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P.S.

D. [

(N/m

)2 /Hz]

P.S.D. of the fluctuating lift force on stationary cable model (U=6.0m/s)

(b) β=45°


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consequence, as additional similarity between RV and DG, both of RV and DG of yawed/inclined cable can be excited by axial flow. Looking extremely violent vibration of proto-type inclined cable observed in the field, it might be rather difficult to aerodynamically distinguish RV and DG, basing on the generation mechanism of galloping excited in relation with KV mitigation points of views, though difference in the climate-condition, those are with rain or without rain. In conclusion, there might be different phenomenon in cable aerody-namic vibration observed in rainy and windy day, the one is typical RV whose vibration mode is beat phenomenon like snake-motion and which is velocity and amplitude-restricted vibra-tion and mostly observed in the fields. The other one is significantly violent vibration like di-vergent-type galloping up to more than 2.0m as peak-to peak amplitude. The former one is definitely affected by formation of upper water rivulet and the later one might be identical phenomenon divergent-galloping in DG from the point of axial flow.

7 Galloping Generation Mechanism

Nakamura [11] pointed out that the galloping generation-mechanism is interruption of communication between upper and lower separated flows. Because communication of two separated flows can tend to make pressure difference on upper and lower surfaces of cylinder zero. This interrupting communication between two separated flows can be accomplished by following three cases. (1) a long downstream splitter plate, (2) vanishing effect of wake undu-lation at low wind velocity related with LSG and (3) critical geometry at high wind velocity which can produce a reattachment-type pressure distribution caused by separated-flow/edge interaction related with HSG. Taking into account that KV would be produced by communi-cation of upper and lower separated flows, in another expression, KV shedding should pro-mote the communication between two separated flows, therefore, the interruption of this communication between two separated flows should be identical to the interruption of KV shedding. Therefore, it van be explained that mitigation or suppression of KV can excite gal-loping instability.

Figure 13: Water rivulet on prototype scale cable model during rain-wind induced vibration (V=10m/s)


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8 Divergent-type Galloping and Unsteady Galloping Galloping can be classified into two different types, those are divergent-type galloping and

unsteady galloping. Former one corresponds conventionally well known galloping, and its response characteristics can be explained by quasi-steady theory. If KV is sufficiently and in stationary suppressed, separated flow is released from the control of KV, then separated flow is so sensitive against external disturbance or stimulation, such as body motion, fluctuating coming-flow, applied sound and so on. Therefore, the mechanism of divergent-type galloping is appearance of motion induced-flow field which is released from KV influence. During downward motion of cable, down-side flow approaches to cable surface, on the contrary, up-per flow leaves from cable surface. Thus down lift can be generated and self-excited vibration appears. The generation mechanism from the point of flow field, this galloping mechanism is substantially identical with the one of low-speed-galloping of bluff body with splitter plate studied by Nakamura [18]. On the other hand, as far as unsteady galloping, if KV mitigation is not sufficient for stationary, cross flow response shows unsteady response with non-stationary amplitude. When KV is mitigated, response amplitude becomes large, on the con-trary when KV sheds, amplitude becomes small. To confirm these characteristics a perforated splitter plate (PSP see Fig.14) is installed in wake center of non-yawed (β=0°) circular cylin-der, cross flow response varies with change of perforation ratio (PR) of splitter plate as shown in Fig.15. PSP can mitigate in stationary KV shedding, stationary galloping with steady am-plitude is generated. As decreasing PR, galloping instability becomes more unstable. As show, it should be noted that the maximum amplitude of vortex-induced vibration near resonant re-duced velocity, Vr=1/St, becomes large as decrease of PR because of more mitigation of KV shedding. On the contrary, as far as unsteady galloping of yawed cable with smooth surface can be observed by wind tunnel test as shown in Fig.16 (described blow in detail). As shown, KV shedding is unsteadily mitigated by axial flow and response amplitude varies according to the intensity of KV shedding.

Figure 14: Characteristics a perforated splitter plate

P.R. 90% P.R. 60%

P.R. 40% P.R. 10% (a) Perforated splitter plates

(View from the downstream side)

0 10 20 30 40 50 60 70 80 90 1000

0.05

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0.15

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Open ratio of splitter plate [%]

Fluc

tuat

ing

win

d fo

rce

coef

ficie

nt C

L′

(b) Fluctuating lift force coefficient of the cable model (β=0°, U=6.0m/s)


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9 Wind tunnel tests in terms of Scruton number Sc vs. reduced critical velocity Vrcr. of galloping characteristics of yawed cable with β=45º

Under three different cable-surface conditions, those are smooth surface, with axial protu-berances, helical fins and with rings, free vibration tests were carried out in smooth flow. The diameters of these are 50mm, and suitable size windows with 100mm in diameter are holed on both wind tunnel walls were installed to promote axial flow in near wake. The measured cross-flow response shows unsteady galloping with unsteady amplitude or divergent–type gal-loping depending on Scruton number as shown in Fig.17 (for smooth surface cable). The other surface cases were fundamentally identical to ones of smooth surface. Unsteady ampli-tude of cross flow response at velocity of 4m/s varies shows fairly good correlation with KV mitigation as shown in Fig.16. If typical divergent-type galloping is not observed, the reduced critical velocity is determined as the lowest reduced velocity where double amplitude exceeds 40% of diameter, D, it means 0.4D. If Scruton number is enough small such as 1.22, diver-gent-type galloping was observed, which is caused by KV in the case of circular cylinder complete suppression due to large amplitude itself. Fig.18 shows KV mitigation by response measured by forced vibration test. But majority results indicate unsteady galloping under lar-

0 1 2 3 4 5 6 7 8 9 10 11 12 13 0

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802A/D 2A [mm]

U [m/s]

U/fD

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P.R.: 100% P.R.: 90% P.R.: 80% P.R.: 70% P.R.: 60% P.R.: 50%

P.R.: 40% P.R.: 30% P.R.: 20% P.R.: 10% P.R.: 0%

Figure 15: Velocity – Amplitude diagrams with various perforated splitter plate (β=0°, D=50mm, in smooth flow. P.R.: Perforated ratio)

Figure 16: Free vibration test results used cable model with smooth surface (β=45°, D=54mm, Sc=1.22, in smooth flow, 200mm window)

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f = 2.57Hzm = 0.660kg/mδ (2A=10mm) = 0.003Sc (2A=10mm) = 1.22

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(a) V-A diagram (b) Time history of fluctuating velocity and amplitude (U=4.0m/s)

: R.M.S. (5 [sec.]) of fluctuating wind velocity ( fk B.P.F.) : Amplitude of cross-flow response ( f0 B.P.F.)

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.S. o

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ty [m

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plitu

de [m

]

Weak KV

Small Amplitude

Large Amplitude

Intensive KV


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ger Sc than about 20. Some test results, associated with Sc-Vrcr. are indicated in Fig.19. Fur-thermore, by use of test result in terms of Scanlan derivative H1* obtained by forced vibration, as explained by following Eq.(1), (2) and (3). Thus, Sc-Vrcr. characteristics are obtained as shown in Fig.19. As shown, test results obtained from free-vibration tests and forced vibration tests shows fairly well good agreement with Saito criterion. As a matter of fact, wind tunnel data obtained by Saito using proto-type cables with 150mm diameter and approximately 10m length in large-scale wind tunnel, is also associated to not divergent-type galloping but un-steady galloping. Saito describes to author’s inquiry that the determination of Vrcr. is also threshold velocity crossing 40% p-p amplitude. Thus it can be concluded that Saito criterion at larger Scruton number in Sc-Vrcr. should correspond unsteady galloping.

+=++22

1 *4

*1

2

DkH

UkHDUkcm ηηρηηη ηη

&&&& (1)

αddC

kH F1*

1 −= (2)

*12 2

2 HDmSc πρ

δ== (3)

Figure 17: Velocity – Amplitude Diagrams (β=45º, D=50mm, L=1400, in smooth flow, 200mm window)

Set up for cable model

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0 20 40 60 80 100 120 140

0 2 4 6 8 10 12 140

0.2

0.4

0.60.8

1

1.2

1.42A/D

U [m/s]U/fD


0 20 40 60 80 100 120 140 160 180

0 2 4 6 8 10 12 140

0.2

0.4

0.60.8

1

1.2

1.42A/D

U [m/s]U/fD

f =1.67Hzm =1.43kg/mδ (2A=10mm)=0.128Sc (2A=10mm)= 118

0 20 40 60 80 100 120 140 160 180

0 2 4 6 8 10 12 140

0.2

0.4

0.60.8

1

1.2

1.42A/D

U [m/s]U/fD

f =1.76Hzm =1.58kg/mδ (2A=10mm)=0.156Sc (2A=10mm)= 158

0 20 40 60 80 100 120 140 160

Sc=9.89 Sc=25.9

Sc=118 Sc=158 Sc=45.5

Sc=0.97

0 2 4 6 8 10 12 140

0.2

0.4

0.6

0.8

1

1.2

1.42A/D

U [m/s]U/fD

f = 3.10Hzm = 0.450kg/mδ (2A=10mm) = 0.004Sc (2A=10mm) = 0.97

0 10 20 30 40 50 60 70 80 90


12

Figure 18: PSD of Lift force obtained by Forced Vibration tests (β=0º, D=100mm, f=2.5Hz, U=2.0m/s)

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

0.005

0.18 0.19 0.2 0.21 0.22

fD /U

PSD

Lift

[(N

/m)2 /H

z]

stationary0.1D

0.2D

0.3D0.4D

0.5D

0.6D

0.7D0.75D

0.8D

0.85D0.9D

Amplitude of forced vibration 2η

Frequency of forced vibration

Frequency of Karman Vortex

0

10

20

30

40

50

60

70

80

90

100

0 0.05 0.1 0.15 0.2 0.25 0.3

fD /U

PSD

Lift

[(N

/m)2 /H

z]


13

10 Sc-Vrcr. characteristics for observed for proto-type inclined stay-cables in the field Recently, some DG phenomena, including violent cable vibration under precipitation, have

been observed in Japan. Typical DG occurred recently in Japan under without rain state. This cable-stayed bridge has curved bridge girder, therefore the longest stay cables are stayed di-rectly on the ground. One longest cable showed violent vibration as shown in Fig.2, whose p-p amplitude is over than 1.5m, then hit the girder. Bridge girder, handrail and stay cable are seriously damaged. One of four cases is large scale cable elastic model with 30m length in the field, structural dynamics and climate conditions were comparatively verified. For these four cases, their cable vibration look divergent–type galloping because of their significantly large amplitude. These data are plotted on the Sc-Vrcr. diagram by use of measure structural-dynamic data. As shown in Fig.20, these data look to fit to Saito criteria. However there are uncertainties on evaluation of their structural damping. For Bridge A, inspection after violent cable vibration found totally damage of the installed oil damper as shown in Fig.21. But same oil dampers installed to another stay cables which did not vibrate showed oil leakage. There-fore, it is natural to make estimation of that before DG the installed oil damper already had not done work well as damper. If so, cable structural damping should be much smaller than indicated in Fig.22. The other two cases cable structural damping are unexpectedly large, be-cause cable structural damping of another stay cable showed much smaller such as δ=0.003 or 0.005 from test carried out on same day. Therefore if as cable structural damping of these three cases, δ=0.005, which is mostly reasonable value for general stay-cables, would be used, their Scruton numbers are revised, then their plots on Sc-Vrcr. shows fairly good agreement with FHWA criterion. Therefore, FHWA criterion on Sc-Vrcr. diagram should correspond divergent galloping.

Figure 19: Comparison of galloping onset velocity (β=45°, Smooth cable, in smooth flow)

0

50

100

150

200

250

300

350

0 30 60 90 120 150 180Scruton Number (Sc=2mδ/ρ D 2)

Ons

et re

duce

d ve

loci

ty (V

r=U

/fD)

FHWA’ criterion

Saito’ criterion

: Based on H1*

: Free vib. tests : Saito’ plot


14

Figure 20: Field observation data at proto-type stay cable of cable-stayed bridges

050

100150200250300350400

0 30 60 90 120 150 180Scruton Number (Sc=2m δ /ρ D 2)

Ons

et re

duce

d ve

loci

ty (V

r=U

/fD)

: Saito’ criterion : Saito’ plot : FHWA’ criterion

Bridge C

Bridge B

Kushimoto Bridge A

Figure 21: Damaged oil damper

Figure 22: Field observation data at proto-type

050

100150200250300350400

0 30 60 90 120 150 180Scruton Number (Sc=2m δ /ρ D 2)

Ons

et re

duce

d ve

loci

ty (V

r=U

/fD)

Bridge C

Bridge B

Kushimoto : Saito’ criterion : Saito’ plot : FHWA’ criterion

Bridge A


15

11 CONCLUSION In conclusion, it is verified that the dry galloping is caused by mitigation of Karman vortex

(KV) shedding, which is fundamentally identical mechanism of galloping by interruption of communication between two separated flows by motion-induced self-excited vibration associ-ated to low speed galloping of rectangular cylinder or circular cylinder with splitter plate in near wake pointed out by Nakamura. Furthermore, Galloping can be classified into steady gal-loping, including divergent-type galloping, with steady amplitude and unsteady galloping with unstable amplitude corresponding KV mitigation level. In Sc-Vrcr. diagram, FHWA cri-terion and Saito criterion correspond steady galloping and unsteady galloping, respectively.

REFERENCE [1] M. Matsumoto, T. Yagi, Q. Liu, T. Oishi and Y. Adachi. Effects of axial flow and Kar-

man vortex interference on dry-state galloping of inclined stay-cables. Proceedings of the 6th International Symposium on Cable Dynamics, Charleston, South Carolina, U.S.A., September 19-22, 2005, 247-254.

[2] M. Matsumoto. Observed behavior of prototype cable vibration and its generation mechanism, Bridge Aerodynamics. Proceedings of the International Symposium on Ad-vances in Bridge Aerodynamics, Copenhagen, Denmark, May, 1998, 189-211.

[3] M. Matsumoto, N. Shiraishi and H. Shirato. Rain-wind induced vibration of cables of cable-stayed bridges. Journal of Wind Engineering and Industrial Aerodynamics, 41-44, 1992, 2011-2022.

[4] S. Cheng, P.A. Irwin, J.B. Jakobsen, J. Lankin, G.L. Larose, M.G. Savage, H. Tanaka and C. Zurell. Divergent motion of cables exposed to skewed wind. Proceedings of the 5th Int. Symposium on Cable Dynamics, Italy, September 15-18, 2003, 271-278.

[5] G.L. Larose, J.B. Jakobsen and M.G. Savage. Wind-tunnel experiments on an inclined and yawed stay cable model in the critical Reynolds number range. Proceedings of the 5th Int. Symposium on Cable Dynamics, Italy, September 15-18, 2003, 279-286.

[6] M. Matsumoto. Vortex-excited vibration and galloping instability of inclined cables. 6th Italian Conference on Wind Engineering, IN-VENTO-2000, Genova, June 18-21, 2000.

[7] M. Matsumoto, Y. Hikami and M. Kitazawa. Cable vibration and its aerodynamic me-chanical control. Proceedings of the International Conference IABSE, Vol.2, Deauville France, October 12-15, 1994, 439-452.

[8] T. Saito, M. Matsumoto and M. Kitazawa. Rain-wind excitation of cables on cable-stayed Higashi-Kobe Bridge and cable vibration control. Proceedings of the International Conference A.I.P.C.-F.I.P. Cable-Stayed and Suspension Bridges, 1994, 507-514.

[9] M. Matsumoto, T. Yagi, H. Hatsuda, T. Shima and M. Tanaka. Sensitivity of dry-state galloping of cable stayed bridges to Scruton number. Proceedings of the 7th International Symposium on Cable Dynamics, Vienna, Austria, December 10-13, 2007, 331-338.

[10] FHWA/HNTB. Wind induced vibration of stay cables. Interim final report, RDT 05-004, 2005.

[11] Y. Nakamura and K. Hirata. The Aerodynamic Mechanism of Galloping. Transaction of the Japan Society for Aeronautical and Space Science, Vol.36, No.114, 1994, 257-269.

[12] M. Matsumoto, K. Yokoyama, T. Miyata, Y. Fujino and H. Yamaguchi. Wind-induced cable vibration of cable-stayed bridges in Japan. Proceedings of Canada-Japan Joint Workshop On Bridge Aerodynamics, 1989, 101-110.

[13] M. Matsumoto, N. Shiraishi, M. Kitazawa, C.W. Knisely, H. Shirato, Y. Kim and M. Tsuji. Aerodynamic Behavior of Inclined Circular Cylinders -Cable Aerodynamics-. In-


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ternational Colloquium on Bluff Bodies Aerodynamics and Applications, Elsevier, 1990, 63-72.

[14] M. Matsumoto, C.W. Knisely, N. Shiraishi, M. Kitazawa and T. Saitoh. Inclined-Cable Aerodynamics. Proceedings of Structural Design, Analysis & Testing, Structures Con-gress ’89, ASCE, 1989.

[15] G. Schewe. On the force fluctuations acting on a circular in crossflow from subcritical up to transcritical Reynolds numbers. Journal of Fluid Mechanics, vol.133, 1983, 265-285.

[16] S. Cheng, P.A. Irwin, J.B. Jakobsen, J. Lankin, G.L. Larose, M.G. Savage, H. Tanaka and C. Zurell. Divergent motion of cables exposed to skewed wind. Proceeding of the 5th Int. Symposium on Cable Dynamics, Santa Margherita Ligure, Italy, September 15-18, 2003, 271-278.

[17] J.H.G. Macdonald. Quasi-steady analysis of 2DOF inclined cable galloping in the criti-cal Reynolds number range. Proceedings of the 6th International Symposium on Cable Dynamics, Charleston, South Carolina, U.S.A., September 19-22, 2005, 435-442.

[18] Y. Nakamura, K. Hirata and T. Urabe. Galloping of rectangular cylinders in the presence of a splitter plate. Journal of Fluids and Structures, Vol.5, 1991, 521-549.

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