IJ'!I"""'

VORTEX INDUCED CABLE VIBRATIONS

Shyang-Yu Baur* Min-Chih Huang** Chia-Chuen Kao***

ABSTRACT

In this paper the experimental results of vortex induced vibrations

(strumming) of bare cables made of nylon synthetic fiber ropes are presented.

Measured vortex shedding 8trouhal numbers and foree coefficients for strumming

cabIes ln a steady unlform f low are obtained from a seIf excitationexperiments.

The mean vortex shedding 8trouhal numbers are 0.171 and 0.168 for the

cable under 20 and 10 kg pretensions ，respectively. In general the vortex

shedding results in alternating lift forces at the fundamental 8trouhal

frequencies ，while the inline drags alternate at the second harmonics. Large

transverse f?rces with lift coefficient as high as 3.897can be induced by

cab le strummlng.These force coefficIents ，bbtalned from SUITIIRIn9the force

amplitudes in an interval centered at the spec1:rum peaks ，can be used to

simulate the measured force for most cases with narrowband spectrums.

INTRODUCTION

8trouhal (1878) first discovered a relati.onship between the vortex

sheddi.ng frequency (fo) ，cyliner diameter (0)，and the velocity of the ambient

fl ow (U).A dimerlslonl ess number can be used to def ine thls re 1at Ionship as

So =fo D/U，where So is known as strouhal number .The a lternate vortex

shedding resul ts in an oscl l l atingtransverse force in a di rection away from

?he last detached vortex on the ri9MIy fixed cylinder.Thls transverse lift

主orce exists practically at all Reynolds number. At subcritical Reynolds

numbers，the strouhalnumber is about 0.2for smooth cylInder.At crlt icaI

regime ，when the cylinder is free to oscillate ，the 8trouhal number remains at

a value nearly equal to that found at subcritical Reynoldsnumbers [Lienhard(1966)].

*Graudate Student ，Department of Hydraulic & Ocean Engineering ，NationalCheng Kung University

MASS?ciate Professor ，Department Of Naval Archltecture&Manne Engineering ，National Cheng Kung Univers'ity⋯::::;立λ:::::;:一Oepa巾 ent of Hydraulic & 06ean Engine叫 \g，National

一635一

structura1 resonance often occurs when the vortex shedding frequency is

near the natura1 frequency of the structure. Numerous experiments have shown

that when the vortex shedding frequency brackets the natura1 frequency of an

e1astica11y mounted structure ，the structure takes contro1 of the shedding in

apparent vio1ation of the Strouha1 re1ationship ，where the interaction between

the structura1 osci11ation and the f1uid action is non1inear. This phenomenon

often encompass a range of 25 to 30 屯 of the natura1 vortex shedding frequency

[Sarpkaya & Isaacson (1981)].

Cab1es are high1y non1inear structures. The non1inearities are due to

inherent properties of cab1e responses ，such as 1arge disp1acement ， 1ack of

stiffness in f1exure and compression ，and constitutive re1ations. The

adaptive nature of cab1es often makes them more vu1nerab1e to vortex induced

vibrations.

Marine cab1es made of synthetic fiber ropes are constructed by twisting

severa1 strands around each other he1ica11y. This he1ica1 shape introduces

disturbances on the surface which interact with the vortex shedding

mechanicsm ， and the wake structure becomes more comp1icated. The vortex

induced cab1e vibrations may be studied experimenta11y by se1f excitation or

forced vibration of the tested cab1e ，since the simi1arities in the wake

structures from these two experiments were va1idated by Griffin (1972).

Recent studies inc1ude those of Pe1tzer (1983) ，Pe1tzer & Rooney (1984) ，Griffin & Vandiver (1984) ，Vandiver ~ Chung (1989).

The osci11ations of marine cab1es caused by vortex shedding ， common1y

termed as cab1e strumming ，resu1t in 1arger hydrodynamic forces ， increased

fatigue and amp1ified acoustic f10w noise ，and sometimes 1ead to structura1

fai1ures. Since cab1e supported structures become increasing1y important to

the ocean re1ated app1ications ，the phenomenon of cab1e strumming needs to be

studied more extensive1y. In this paper the strumming of bare cab1es made of

ny10n synthetic fiber ropes are discussed.

TEST SETUP AND bATA ANALYSIS

The present experiments were conducted at the horizonta1 circu1ation tank

of the Fishing Boat and Marine Engineering Research Center ，NCKU. The test

section of this tank is 3.8 m 1ong，1.2 m wide and 0.825 m deep. Steady f10ws

with speeds up to 1.5 m/s can be generated in the test section.

The cab1es that were used in the tests are constructed of nylon synthetic

fiber ropes. A pre1iminary test program was carried out to identify the

pertinent strumming characteristics. A three-components dynamometer was he1drigid1y at the center top of the.test section ， with an universa1 joint

attached be1ow. Each tested cab1e was connected at the top to the universa1

joint and was pretensioned by a sinker at the bottom. Two sinkers with the

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same outer geometry but.with different weights were used in the tests ， one

weights 11.5 kg (in air) whi1e the other weights 23 kg. The hydrodynamic

effect of the two sinkers are the same whi1e giving different stiffness for

the test cab1es. A tota1 of four cab1es with diameters 1.15 ，1.46 ，1.95 and

2.10 cm were used. The test setup is i11ustrated in Fig. 1a.

The dynamometer was pre-ca1ibrated and then used to measure the in1ine

and transverse forces on the cab1e system. The ana10g signals from the

dynamometer were amp1ified and fi1teredthrough a 100 Hz 10w pass fi1ter ，digita1 force measurements of 12 seconds at a samp1ing rate of 50 Hz were then

obtained from an A/D converter and stored for da.ta ana1ysis. A tota1 of 5f2

discretized data points was ana1yzed in FFT a1gorithm to ca1cu1ate the in1ine

and transverse force spectrums from f = 0 to 25 Hz with the frequency

reso1ution of 0.0977 Hz.

The fi1tered ana10g signa1s from the dynamometer were a1so connected to a

dua1 channe1 Ono-Sokki Spectrum ana1yzer where the force spectrums averaged

from 256 consecutive runs were stored and compared with the FFT spectrums.

The averaged smooth spectrums ，compared c1ose1y with the FFT spectrums ，were

used on1y to identify if the f10w conditions were too disturbant or not.

One meter upstream of the tested cablE!，a simp1e mechanism was

constructed to 10wer and current meter to any vertica1 position in the tank.

The current meter was a Marsh-McBirney Mode1 523，dua1-ax 土s， e1ectromagnetic

type. The sensor outputs were passed through 10w pass fi1ters. A time

constant of 5 seconds ，with a 3dB corner frequency of 0.0306 Hz，was set

during the tests. The uniform steady currents ~Iere measured 0.1 m be10w the

free surface after force measurements were taken 。

In genera1 ，the resu1ts from this pre1iminary test program revea1 that:

(1) The transverse force spectrums are most1y narrowband.

(2) At transition ，the shedding process are slight1y broadband.

(3) For the sma11er two cab1es at higher tension ， transition occurs

approximate1y at Reyno1ds number betweE!n 10500 - 15000; at 10wer

tension ，transition occurs at Reynolds number between 9000 - 12000.

(4) For the 1arger two cab1es at higher tension ， no transition was

observed; at 10wer tension ，transition occurs at Reyno1ds number

between 20500 - 24500.

(5) At 10w tensions ，the tested cab1es were more vu1nerab1e to strumming.

At subcritica1 Reyno1ds numbers ，the shedding proc

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transition the upper and 10wer bonds of Strouhal. number are p10tted instead ofthe average va1ues.

As summarized by Vandiver & Chung (1989) ，the prediction of the response

of a cab1e system to vortex shedding may be thought of as consisting of fourmajor components:an excitation mode1，a structura1 model ，a damping mode1，and

a solution technique. For examp1e，wake osci11ator mode1 for transverse

osci11ations was deve10ped by Griffin et a1. (1975) for predicting the 1ift

coefficient as a function of time. This paper emphasizes the measurement and

prediction of excitation mode1. The information provided by the pre1iminary

tests are however 1imited ，e. g. ，the effect of the sinker on the force

coefficients can not be accurate1y accounted for.

The test arrangement was therefore improved by using a bending type 10ad

ce11 (Kyowa Model LUB-50KB) rigid1y mounted at the tank bottom ，a swive1 was

connected to the 10ad ce1l where the tested cab1e can be simp1y connected ，as

i11ustrated in Fig. 1b. The cab1e was pretensioned and adjusted at the top

through a turnbuck1e. The cab1e that was used in the tests has a diameter of

2.10 cm. During the first test sequence the cab1e tension was origina11y

adjusted at 20 kg，then the tests were carried out from 10wer f10w speeds to

higher speeds. A residua1 tension of 9.9 kg was measured after the tests with

no f1ow. During the second test sequence the cab1e tension was origina11y

adjusted at 10 kg and a residua1 tension of 7.5 kg was measured after the

tests. Tab1e 1 summarizes the mean tension on the test cab1e obtained from

FFT ana1ysis of the 10ad ce11 output for each test runs. Resu1ts from these

two test sequences are discussed in the next section.

RESULTS AND DISCUSSION

The transverse force amp1itude spectrums for the tested cab1e under 20

kg pretension at various speeds are i11ustrated in Figs. 3a - 3c. The

transverse force amp1土tude spectrums for the tested cab1e under 10 kg

pretension at various speeds are i11ustrated in Figs. 4a - 4c. Each figure

contains six spectrums to i11ustrate the variation of vortex shedding process

with increasing current speeds. It is c1ear1y shown in these figures that the

shedding frequency increases when the current speed is increased. Transition

occurs approximate1y at Reynolds number between 25500 - 31300 (corresponding

to fi1es C194 ~ C198) for cab1e under 20 kg pretension ，and occurs at Reyno1ds

number between 23000 - 27000 (corresponding to fi1es C211 - C214) for cab1eunder 10ιkg pretension.

The variation of Ströuha1 number with Reyno1ds number from the improvedexperiments is i11ustrated in Fig. 5，where at critica1 regime an average

Strouha1 number was ca1cu1ated fromeach force spectrum to quantify the

broadband shedding process. The mean Strouha1 numbers are 0.171 and 0.168 for

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cab1e under 20 kg and 10 kg pretensions ，respect 土ve1y，throughout the Reyno1ds

number range 12000 to 35000. For comparison ，a va1ue of 0.192 was obtained by

Pe1tzer (1983) for Kev1ar ropes wrapped with a po1yurethane jacket throughout

the Reyno1ds number range 2000 to 42000.

The transverse 1ift force coefficients for the strumming cab1es are

presented in Figs. 6a-6b ， for cab1e under 20 kg and 10 kg pretensions ，respective1y ﹒The in1ine force coefficients are presented in Figs. 7a-7b ，for

cab1e under 20 kg and 10 kg pretensions ，respective1y. The mean 1ift and drag

coefficients ，CL(O) and CO(O)，were ca1cu1ated direct1y from the FFT ana1yses

of force measurements. The fundamenta1 1ift and drag coefficients ，CL(l) and

CO(l) ，were obtained by first 10cating the vortex shedding frequency ，fo ，from

each spectrum; then the force amp1itudes in an interva1 of 40 frequency

increments (i.e. ，3，906 Hz) centered at fo were summed together as the peak

amp1itude for the representative narrowband spectrum. The force coeff 主cients

for the higher harmonics ，e.g. ，CL(2) and CO(2)，were ca1cu1ated simi1ar1y ﹒Figs. 6 - 7 indicate that:

(1) In genera1 the vortex shedding resu1ts in a1ternating 1ift forces at

the fundamenta1 frequencies ，whi1e the in1ine drags a1ternate at the

second harmonics.(2) The vortex shedding does not necessari1y resu1t in a symmetric 1ift

force variation ，主.e. ，mean 1ift coefficient ，CL(O)，is not necessari1y

zero.(3) The variations of force coefficients are found to be simi1ar for the

two cab1e pretensions studied.

(4) Large 1ift forces can be induced ，e.g. ， the fundamenta1 1ift

coefficient is as high as 3.897 for cab1e with 10 kg pretension at f10w

speed U = 72 cm/s (Fi1e C207)，whi1e the mean drag coefficient is on1y

1. 607.These force coefficients can be used to simu1ate measured force

variations' for most cab1e strummings with narrowband spectrums. Fig. 8

i11ustrates the c10se agreement between the simu1ated and measured transverse

force for cab1e with 10 kg pretension at f10w speed U = 80 cm/s (Fi1e C209).

Evident1y ， the characterization of the vortex shedding proceSB by a simp1e

(fundamenta1) frequency and its harmonics is a practica1 simp1ification ，

especia11y at transitions. An examp1e is given in Fig. 9 for cab1e with 10 kg

pretension at f10w speed U = 104.5 cm/s (Fi1e C214) where the corresponding

force spectrum is broadband.

CONCLUSIONS

In this paper the vortex induced vibration of bare ny10n eab1es are

studied experimenta11y by se1f excitations of the cab1e in steady uniform

一639一

f1ows. In the pre1iminary tests ，cab1es were pretensioned by free pendu10us

sinkers of 23 and 11.5 kg (in air) at bottom. In the improved tests ，cab1es

were simp1y connected at both ends and pretensioned at 20 and 10 kg.respective1y.

Prior to and after transitions ，the vortex shedding process can be

identified by a single fundamenta1 frequency from the measured force spectrum.

At transitions on1y an average va1ue ，or upper and 10wer bonds ， for the

shedding process can be defined ﹒The variation of vortex shedding Strouha1

number versus Reyno1ds number obtained from the improved tests 1ie between the

corresponding upper and 10wer bonds obtained from the pre1iminary tests.

Experimenta1 resu1ts from the improved tests indicate that:

(1) The mean vortex shedding Strouha1 numbers are 0.171 and 0.168 for cab1eunder 20 and 10 kg pretensions.

(2) Large transverse forces can be induced by cab1e strumming ， therefore ，suppression devices shou1d be considered in severe conditions.

(3) Force coefficients ca1cu1ated from summing the force amp1itudes near

the spectrum peaks can on1y be used to simu1ate the strumming force

vibrations with narrowband spectrum. An improved deterministic mode1

or a statistica1 ana1ysis based on the spectra1 content is required at

transitions in order to better simu1ate the vortex shedding process.

REFERENCES

1. Griffin ， O.M﹒1972. F10w near se1f-excited and forced vibrating circu1ar

cy1inders. J. Engrg. for Ind. ，ASME，Vo1.94 ，539-548.

2. Griffin ，O.M.，R.A. Skop &S.E. Ramberg. 1975. The resonant ，vortex-excited

vibration of structures and cab1e systems. Proc﹒ 7th OTC. Paper OTC 2319.

3. Griffin ， O.M﹒& J.K. Vandiver ，1984. Vortex induced strumming vibrations

of marine cab1es with attached masses. Proc. 3rd OMAE，Vo1.1 ，300-309.

4. Lienhard ，J.H. 1966. Synopsis of 1ift ，drag and vortex frequency data for

rigid circu1ar cy1inders. Washington State Univ. ，Co11ege of Engrg. ，Res.Div. Bu11etin 300.

5. Pe1tzer ， R﹒D. 1983. Vortex shedding in a 1inear shear f10w from a

vibrating marine cab1e with attached b1uff bodies. Proc. 2nd OMAE﹒ 147-155.

6. Pe1tzer ，R.D﹒& D.M. Rooney，1984. Near wake properties of a strummina

marine cab1e: an experimenta1 study. Proc. 3rd OMAE，Vo1.1，310-317. 可

7. Sarpkaya ，T﹒& M. Isaaqson ，1981. Mechanics of wave forces on offshorestructures. Van Nostrand Reinho1d Co.

8:;;;::11.s::::; 止;，e;:; 立ondere Art der Ton⋯gu略 A几 Phys. und

9. Vandiver ， J.K ﹒& T.Y﹒Chung，1989. Hydrodynamic damping on f1exib1e

一640一

cylinders in sheared flow. J. Wtrway. Port. Coast. and Ocean Engrg.. ASCE.Vol.115(2). 154-171.

Table 1. SUMMARY OF CABLE MEAN TENSION

F110 1/0. Mean T.nlJ1on (Xq) F11﹒凶。. M".n T.n.ion (JCIjJJ

C182 19.75 C20‘ 可 1，80C183 19.79 C205 H.‘3C184 19.83 C206 13.37C185 19.85 C207 13.89C186 19.79 C208 14.39C187 19.63 C209 14.75C188 19.3‘ C210 14.19C189 19.68 Cl11 13.75C190 19.96 C212 13.99C191 20.05 Cl13 14.11C192 20.12 Cl14 14.34C193 18.86 Cl15 16.78C19. 19.16 Cl16 17.55C195 19.10 C217 18.60C196' 19.40 Cl18 18.84C197 19.69 C219 19.69C198 20.01 C220 20.15C199 19.91 C221' 19.32

1. DYNAMOMETER

2. FREE SURFACE

3. CABLE

4. SWIVEL

5. S工NKER

6. LOAD CELL

-‘2

'，叫80S 即四

T1M.

Fig. la. Preliminary test setup Fig. lb. Improved te'st setup

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0.50

CABLE DIAMETER.= 1.15，1.46，1.95，2.10 CMSINKER WEIGHT = 11.5，23.0 KGFILE : C1 - C171

0.40

O三三

-l0.30〈工2

2ω←(f)

0.10

s• X ..L~一九.、益，向全呵呵eht驗。。o .~ .•. A 字

。宜。可

0.00103

RE丫NOLDS NO.10 •

Fig. 2. Variation of Strouhal number with Reynolds number from

preliminay experiments

0.6

r-\OAζ、、、./

~~'?'::.F;，..~Á:. ._=:，_ ?:..! (CM)CURRENT VELOCI1Y '= 46.592.!._~?~~~!.-l?'?!1] iÇ~/s)( FROM BOTroM TO TOÞ')

PRETENSION = 20 KGFILE : C182-C187

Q..

εO

1 il.. 且， Jh‘-.四、.--♂，神............戶.ρ ‘一一、l _____‘-_____..'~..._~__--司--一-......

353025(hz)

15freq

10

..----，.‧‧.，..!"'，-_........-----------------j___w - ""_.-.._______________________...____________、----

5

Q)υL '1

.E 0.2 ~

0.0O

cncok一+-'

Fig. 3a. Transverse force amplitude spectrums for the

cable under 20 kg pretensionstrumming

-642 一

呵呵 1 、舟， μ""'" 也W

1.2

，-\。可立〈\一/

。-EO

CA8LE 01人=2.1 (CM)CURRENT VELOCITY = 76.80. 84丸 90.5. 95，97 (ÇM/S)( FROM 80TTOM TO TOP )

PRETENSION = 20 KGFILE : C188-C193

ωυ1-

�0.4

(f)CO1--←J

0.0O 5 10 15freq

25(hz)

30 35 ，.

Fig. 3b. Transverse force arnplitude spectrwns for the strurnmingeable under 2日 kg pretension

1.2

/戶『、、。可二望已\一/

CA8LE 01A. = 2.1 (CM)CURRENT VELOCITY = 99.5.10}. _110-，JJ 4，L22 ，~1~9‘(CM/S)( FROM 80TTOM TO TOP )

PRETENSION = 20 KGFILE : C194-C199

353025

ai

1i:l 1Jt r"t ~

"''-~'!‘'jï 丸4、.I_~--- ~I''''，\‘﹒、一-一一一可一..--.--司.、，一-‘..........‘'‘--

frequency (Hz)5

Q.

ED

U】co1--+-'

0.0O

Q)υ1-

�0.4

Fig. 3e. Transverse force ampl itude spectrwns for the strummingeable under 20 kg pretension

一643 一

1.2CABLE DIA. = 2.1 (CM)CURRENT VELOCI1Y = 58 ，62 ，67，72. 75丸 8~( 叫/S)( FROM BOTTOM TO TOP )

353025

PRETENSION = 10 KGFILE : C204 一C209

i'‧‧‧‧

叭l'，‧‧‧'‧.‧..‧‧.'"""".."""...，..-‧‧'丸，、.-"，.-..、.-10..____-"'_______

frequency (Hz)

斗1--' 一}一一一一一

'5

i'~ft--~j尺

司 ~___J\.---' '..‘---..._--_..、----‘------，----﹒‘---------------.

Q)υL

20.4

0.0O

。-EO

/戶『、。可」豆、-/

Fig. 4a. Transverse force ampl ìtude s~ctrums for the strummingeable under 10 kg pretension

0.8CABLE DIA. = 2.1 (CM)CURRENT VELOCI1Y = 84 ，89.5 ，-94.5. 102 ， 104.5 ， '104 (CM/S)( FROM BOTTOM TO TOP )

‧‧'，"，'"l'""""11"jk i

":~4\^;.! ?'"、白，叫_.._J ‘_..........一.ι一----一、叫“:f1l......，.，

PR凹:ENsf(l)N = 10 KGFltE : CZ1。一C215

/戶『、。可去己的

。-EO 0.4ωυLO斗一

ui 0.2COL+J

5 frequency (Hz) 25 30 3'5

Fig. 4b. Transverse force amplitude spectrums for thecable under 10 kg pretension

str山lUung

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frequency (Hz)

CABLE DIA. = 2.1 (CM)CURRENT VELOCITY = 108，110. 120_. 1_25. ~30. 135:5 (CM/S)( FROM BOτfOM TO TOP )

1.2

/戶『、、

o~、-..‧-/

0...

EO

(1)uL

�0.4

0.0 o

PRETENSION = 10 KGFILE : C216-C221

5 25 30 35

0.5

0.4

OZ

Fig. 4c. Transverse force arnplitude spectrums for the strwnming

eable under 10 kg pretension

CABLE DIAMETER= 2.10 CMCIRCLE : PRETENSION 10 KG (FILE : C204-C221 ).STAR : PRETENSION 20 KG "( FILE : C182-C199)

一J 0.3〈工3

2。2←(f)0.1

0.0.10 •

會 ‧會

已 ‧

•b。。..-。cρ~^ 例。ö ~ ，t Glr 會'**‧. ，，"， O.foo ........-ôo 會會會"

RE丫NOLDS NO.r-，10 •

Fig. 5. Variation of Strouhal number with Reynolds number

improved experiments

一645一

from

。。。

4

3」uLl..Lw 2O仁J

t-11

O10 •

會

"og

會

自

。。。 。。

。。

。。。

*會

會 . ""。，.盒." a。o ð- ~開會 R恥會會*'。因。 D~: .. *.1"111 aou_::-~

RE丫NOLDS

CABLE DIA.= 2.1 CMPRETENSION = 20 KGFILE : C182 一 C199

STAR : CL .cQ)CIRCLE : CL (1)RECTANGLE : CL (2)TRIANGLE : CL 口7

10 •NO.

Fig. 6a. Transverse lift force coefficients for the strumming

cables under 20 kg pretension

4 。。。 。 CABLE DIA.= 2.1 CMPRETENSION = 10 KGFILE : C204 一 C221

。

。。.。。

。

3一」已J

l..Ll..Lw 2O已〉

t

。 。

。。。。

。。

STAR : CL '<Q)CIRCLE : CL (1)RECTANGLE : CL (2)TRIANGLE : CL (3y

O10'

會 4‘會" - -，..Ahaaa M

~... n:~~~lIl ﹒‘﹒.實 .l" .會..000000 團g ••~..

RE丫NOLDS10 •

NO.Fig. 6b. Transverse lift force coef.ficients for the strunming

cables under 10 kg pretension

-646一

4

心 J瓦E

，可

3 CA8LE DIA. = 2.1 CMPRETENSION = 20 KGFILE : C182 - C199INLlNE

會

*STAR : CD J(的CIRCLE : CD l1)RECTANGLE : CD (2)i:RIANGLE : CD (3)"

*。圓

圓

E

‧* * *會.‧‧**‧‧‧

*

會

OζJ

.2l.Ll.LwOζJ

ü<(.匠，。

回

。一t 、r(j'~

3

OιJ

。-2...zha n

R! ，l 曲.，-suo-eB' ，- r--，10 e

CA8LE DIA. = 2.1 CMPRETENSION = 10 KGFILE : C204 一 C221INLlNE

.2l.LLwOζJ

仁3〈句匠，

O

* • • **‧包，也

自

a

會

會，會..會

臨LE::::3

a

o10:4'

。-rP 。﹒'。

E' ，zzs -tB b 圓圓圓。

REYNOLDS

r--，10 e

NO.E主g. 7b. Inline drag force coefficients for the strumming cables

under 10 kg pretens ion

-647一:'

1.0

r-\仁DX\-/ 0.5

μJ仁J佐

OLL 0.0

~ h h ~ e有，.A

"11

'，自

501，10:以PE~IMENT (們LE : C209 )DA5l'f:所(P日K AVERAGED -)-，

一1.5rÎ..j ''-i j 1.1-..1..1 i

O.lJ .. .0;區 1.H1 起 ..iH ‘a a.. a-iEEB..a..1.bTIME (S)

Fig. 8. Sirnulat 立。n of measured transverse force with a narrowband

spectrum

0.6

r-\仁DK三 0.4、'-"

帆，'，'Ii'IiaIia'，'，'，

" r\ n :;~ ~: u wt 111

111'

B11，1111.'‘且，‘'，‘

50叩 :EXPRIME 附 (FlLE : C勾 4 )DASH : FFT ( PEAK AVERAGED 】

0.2

0.0

ι」ιJa:::OLL

ιJ但一0.2w〉

望一0.4〈佐←--0.6

一0.8 于0.0 0.5 1.0 TIME (S) 2~0 2.5 3.0

Fig. 9. Simulation of measured transverse force with a broadband

spectrum

一648一

一可磨哥哥‘川 >!!:Z)'1 叮、， J，r"' .•.•~_~~，'~丹、~

川、 ι

渦流脫落激設之纜繩振動

薄祥裕. 黃明志** 高家俊***

本文探討在祖流水槽中之種態均勻流況下，尼龍纜繩因渦流脫落而激發之自然振動，試驗

之結果包含渦流脫落頻率，史儲福數與各階之正向，側向流體力係數。

直徑 2.1 cm之纜繩在預張力為 20 kg 與 10 kg 時之渦流脫落史儲福數平均值為 0.171 與

0.168 。試驗結果聶示纜繩在渦流脫落頻率附近激發高頻之側向振動，而在渦流脫落頻率之第二階振激發高頻之正向振動。

共振時(渦流脫落頻率與纜繩之自然振頻相近時)之側向振動力係數可高達 3.897 。試驗

結果亦顯示纜繩之正向與側向力頻譜大多為牢頻，是以依攘頻譜各尖峰附近之能量而計算之流

體力係數可用來反算纜繩在各種均勻流況下所承受之正向與側向力。

.國立成功大學水利及海洋工程所研究生

**國立成功大學造船及船船機械系副教授

***國立成功大學水利說海洋工程所副教授

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