wind-induced response of inclined and yawed ice-accreted...

Research ArticleWind-Induced Response of Inclined and YawedIce-Accreted Stay Cable Models

Songyu Cao1 Himan Hojat Jalali 2 and Elena Dragomirescu 3

1Key Laboratory of Transportation Tunnel Engineering Ministry of Education Southwest Jiaotong University Chengdu 610031Sichuan China2Civil Engineering Department University of Texas at Arlington 425 Nedderman Hall 416 Yates St Arlington TX 76019 USA3Faculty of Engineering University of Ottawa 161 Louis Pasteur Ottawa ON K1N 6N5 Canada

Correspondence should be addressed to Elena Dragomirescu elndraguottawaca

Received 23 March 2018 Revised 1 August 2018 Accepted 5 September 2018 Published 9 October 2018

Academic Editor Tai ampai

Copyright copy 2018 Songyu Cao et al ampis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

During the past decades wind-induced vibrations of bridge stay cables were reported to occur under various incipient conditionsampe ice formation on stay cables is one of these conditions which causes the ice-accreted stay cables to alter their cross sectiongeometry thus modifying their aerodynamic characteristics Wind tunnel tests and several CFD simulations were performed forice-accreted inclined bridge stay cables with two ice-accretion profiles dimensions 05D and 1D where D is the diameter of thecable Wind-induced vibrations were analyzed experimentally for cable models with yaw inclination angles of 0deg 30deg and 60deg andvertical inclination angles of 0deg and 15deg for Reynolds numbers of up to 4times105 ampe aerodynamic drag and lift coefficients of thecable models and the pressure coefficients were determined from the CFD-LES simulations ampe experimental results indicatedthat the vertical and torsional vibrations of the ice-accreted stay cables increased with the increase of the vertical and yaw anglesAlso higher vertical and torsional vibration amplitudes were measured for the case with larger ice thickness indicating the effectof the ice accretion profile on the cable wind-induced response

1 Introduction

Cable-stayed bridges are among the most reliable andcomplex bridge structures and their ability to support longspans make them an ideal solution for spanning large dis-tances over bay or valley regions with high vehicular trafficOne of the main concerns when designing such bridges isrelated to the wind-induced effect on the bridge decks andtowers However during the past decades large-amplitudevibrations of stay cables have been reported [1ndash7] ampesevibrations can tamper with the safety and serviceability ofcable-stayed bridges and can cause unexpected fatiguefailures at the cable anchor points ampe causes for the staycable vibrations vary in nature such as rain-wind inducedvibrations [5 8] dry inclined cable galloping [2 9ndash12] andhigh-speed vortex excitation [8 13 14] Another type vi-bration has been reported in recent years for bridge staycables with ice accretion when sudden large-amplitude wind

and ice accretion-induced vibrations were noticed [15ndash18]For this phenomenon the ice accumulates on the stay cablesurface under freezing rain drizzle and wet or dry snowconditions at low temperatures ampe formed ice accretionchanges the cross-sectional shape of the cables which in turncan cause aerodynamic instability [19] Several field studiesreported vibrations of stay cables in freezing conditionswhich caused the ice to detach from the cables and fall on thepassing vehicles ampe Port Mann Bridge in Canada wastemporarily closed to traffic in 2012 because of the ice-accreted cable vibrations and due to the ice falling fromthe stay cables causing a hazard for the traffic and people onthe bridge ampe Tacoma Narrows Bridge in USA was tem-porarily closed in 2011 due to similar hazards caused by thefalling ice from the cables Similar phenomena of ice fallingfrom cables were reported for other bridges as well such asthe Alex Fraser Bridge in 2016 Canada the Great Belt EastBridge Denmark [20] and the Severn Bridge in UK [21]

HindawiShock and VibrationVolume 2018 Article ID 6853047 12 pageshttpsdoiorg10115520186853047

In an attempt to clarify the onset conditions for the ice-accreted cable vibrations Koss andMatteoni [22] conducteda wind tunnel experiment for determining the effect of iceaccretion on the aerodynamic forces recorded for full-scalecables under 0deg angle of attack and Re numbers of up to32times105 using the FORCEDTU climatic wind tunnel(CWT) Also Koss et al [23] performed an experimentalinvestigation for determining the shape of the ice accretionformed on cables of 00381m and 0089m in diameter thatwere oriented in horizontal and vertical directions fordifferent exposure times and air temperatures ampey clas-sified the regions of the ice accretion profiles into the corecenter area outer area flow-out flow-out accumulation andrunback ampe effect of the ice accretion on the aerodynamicsof the vertical bridge hangers was investigated by Gjelstrupet al [20] using static and dynamic wind tunnel tests ampeaerodynamic coefficients were determined for smooth andrough surfaces of the ice-accreted cables under smooth andturbulent wind flow conditions Furthermore Koss andLund [24] presented the results of a full-scale experimentalstudy on horizontal 160mm diameter bridge cables underwet and dry ice accretion conditions using an innovativespray system to determine the aerodynamic coefficients andto evaluate the galloping instability using the Den Hartogcriterion Moreover Koss et al [25] studied the formation ofice accretion on three full-scale horizontal bridge cables withplain helical fillet and indented high density polyethylene(HDPE) cover under wet and dry climatic conditions andthey concluded that gravity plays a major role in the iceprofile formation on the cables under the wet icing con-dition Also this study indicated that only the cable withplain HDPE cover was susceptible to galloping instability asper the Den Hartog criterion Demartino et al [19] extendedthis study to full-scale HDPE vertical and inclined bridgecables and they investigated the process of ice accretionformation the final ice shape and the correspondingaerodynamic drag lift and moment coefficients for differentparameters such as temperature wind speed and yaw angleUsing the experimental data of Demartino et al [19]Demartino and Ricciardelli [26] modelled different gallop-ing vibrations for one degree of freedom (1-DOF) andmultiple degrees of freedom (MDOF) cables and they an-alyzed the stability of bridge cables with ice accretion Re-sults showed that the 1-DOF models usually generateconservative results and the use of dynamic wind tunnelexperiments was recommended to confirm the results ofexisting theoretical models especially for the cases where nosufficient data are available

However the actual wind-induced vibrations for theinclined and yawed cables in regard to the wind directionwhich are very often encountered in practise with ice ac-cretion attached to their surface were not specifically in-vestigated ampe current study examines the aerodynamicbehavior of yawed and inclined ice-accreted stay cables ampestay cable models had vertical inclination angles of 0deg and 15degand yaw angles of 0deg 15deg 30deg and 60deg while the ice accretionprofile thickness were 05D and 10D Wind tunnel windspeeds between 15ms and 15ms were considered toidentify the critical wind-induced cable vibrations

2 Experimental Set-Up and CableModel Configuration

ampeexperimental programwas performed in the suction windtunnel facility of the University of Ottawa Department ofMechanical Engineering (Figure 1(a)) which has a testingsection of 61 cmtimes 92 cm and has three openings on each sideof the testing section used for installing the models and tocoordinate the necessary vertical and yaw inclination anglesfor the cable models ampe maximumwind speed which can beachieved in the wind tunnel is 300ms however for thecurrent experiment the ice-accreted cable was tested for windspeeds of up to 150ms corresponding to a Reynolds numberof 40times105 considering the high amplitude vibrations de-veloped beyond these testing conditions ampe wind speedvaried during the tests from 15ms to 150ms in steps of15msampe blockage ratio was determined as the total area ofthe model normal to the free stream velocity divided by thetotal area of the test section and was found to be 0368times10minus3and 0736times10minus3 for the cable models with 10 cm and 20 cmice profiles respectively According to West and Apelt [27] ifthe blockage ratio is lower than 6 for smooth cylinders withaspect ratios in the range of 4 to 10 the Strouhal number isnot affected and no correction is needed for the aerodynamiccoefficients hence the turbulence intensity would not bea significant concern

An important parameter which can significantly affect thewind-induced response of the cable models during the windtunnel tests is the relative angle of attack between the winddirection and the cable axisamperefore the wind-cable relativeangle as defined by Cheng et al [2] was employed in thecurrent research that is θ cosminus1(cosα cos β) where θ αand β represent the relative wind-cable angle yaw andvertical cable inclination angles respectively (Figure 1(b)) Tosimulate the wind-induced vibrations of the cables eightsupporting springs each of elastic constant k 15Nm wereinstalled symmetrically at the two ends of the cables along thevertical direction as schematically represented in Figure 1(b)Also the position of the cable models was adjusted using thethree circular openings in the wind tunnel lateral wall and bymoving the entire spring support system installed outside thetunnel to adjust for different vertical and yaw angles of attackas shown in Figures 2(a) and 2(b) For flow perpendicular tothe cylinder at 0deg yaw the same location openings were usedfor installing themodel (Figure 2(c)) while for bigger yaw andvertical angles the cable model was installed between themiddle and the last opening with an elevation differencebetween the spring support systems (Figure 2(d))

ampe cable models were scaled to 1 45 from the prototypebridge cable used by Cheng et al [2] for the full-scale windtunnel experiments conducted for the smooth surface in-clined and yawed cylinders Ice accretion profiles witha thickness of 05D and 1D where D is the diameter of thecable model were added on one side of the cable modelsampese dimensions correspond respectively to a cable iceaccretion thickness of 45 cm (05D) and 90 cm (1D) con-sidering the 1 45 scale factor According to Koss et al [23]exposing the cable for 1800 seconds to precipitations underfreezing conditions the ice accretion profile thickness can

2 Shock and Vibration

reach up to 05D ampe ice accretion profiles with thicknessesof 05D and 10D were both tested in the current experimentfor clarifying the critical ice-accreted cable response Inorder to replicate the arbitrary aspect of the ice profileexpandable foam was applied on the cable model ampe iceaccretion simulated by foam showed good geometricalagreement with the models obtained from the climatic windtunnels reported in the literature [23] especially for thetroughs and crests of the ice accretion However the foamalso developed small gaps and indentations the entire iceprofile was corrected by applying aluminium foil and thusthe cable model and the foam ice accretion could betterresemble the ice surface smoothness as it can be seen inFigures 3(a) and 3(b)

ampree cable models were tested for vertical and yaw in-clinations between 60deg and 15deg as follows (Table 1) CableModel 1 (CM1) was the cable perpendicular to the flow (0deg)and had an aspect ratio of 46 a natural frequency of 0395Hzand a Scruton number of 21ampis model was also used for 15degyaw angle tests Cable Model 2 (CM2) was used for verticalangles of 30deg and 60deg and for yaw angles of 0deg and 15deg this hadan aspect ratio of 535 a natural frequency of 033Hz anda Sc 51 For Cable Model 3 (CM3) the aspect ratio was 92and the natural frequency was 029Hz while the Sc numberwas 105 ampis cable model was used for tests with 0deg 30deg and60deg vertical angles and 0deg and 15deg yaw angles ampe yaw andvertical inclination angles were varied by changing the lo-cation of the model from the middle opening to the last or

(a)

α

β

θ

Wind speed

direction

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Cable model

Longitudinal bar

Transverse bar

Ice accretionmodel

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Figure 1 (a) Suction wind tunnel facility (b) spring suspension system

β

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Figure 2 Cable models configuration in the wind tunnel facility (a) front view (b) top view (c) α β 0deg (d) α 60deg and β 15deg

Shock and Vibration 3

first opening as represented in Figure 3 Table 1 summarizesthe experiments performed for different yaw and verticalinclination angles ampe ice accretion profile of 05D was testedfor all three cable models at yaw inclination angles (α) of 0deg30deg and 60deg and vertical inclination angles (β) of 0deg and 15degSince 10D is considered as an extreme case of the ice ac-cretion thickness more tests were performed for the 05D iceaccretion profile which is more often encountered

3 Vertical and Torsional Wind-InducedVibrations of Ice-Accreted Cables

31 Effect of Ice Accretion ickness ampe torsional andvertical vibrations for the ice accreted cables were recordedfor different wind speeds from 15ms to 15ms at intervalsof 15ms Figure 4 shows the response time histories for thevertical and rotational vibrations for the CM1 cable modelat 0deg relative angle with an ice accretion thickness of 05Dampe maximum vertical and torsional responses were mea-sured as 2392mm and 263deg respectively For the modelCM1 at 0deg relative angle with 10D ice thickness Figure 5reports the vertical and torsional vibrations at 15ms forwhich the maximum vertical displacement was 2195mmwhile the maximum torsional displacement was 58deg It isinteresting to note that despite the slight decrease in themaximum vertical displacements recorded for the CM1 at 0degwith 10D ice thickness the maximum torsional responseincreased by a factor of 21 when compared with the CM1model with 05D ice thickness

Figure 6 presents the time histories of vertical andtorsional response of the cable for model CM2 inclined atrelative angle θ 30deg for the wind speed of 15ms In thiscase the maximum vertical displacements due to wind-induced vibration were recorded as 2194mm at 148 sthe maximum vibration amplitude for torsional displace-ment was 313deg at 41 s ampe torsional vibration was increasingsteadily but no strong fluctuations were noticed for thiscase For higher ice accretion thickness of 10D the cablemodel CM2 registered vertical displacement with themaximum value of 273mm while the mean value for thiscase was 2066mm (Figure 7(a)) ampe maximum amplitudeof the torsional vibration was 73deg as it can be noticed inFigure 7(b) and the average value for this case was 33deg

For clarifying the effect of the ice accretion effect on themean vertical displacement of the tested cables for differentwind speeds the response of the same inclination modelsbut with 05D and 10D ice accretion thickness was com-pared in Figures 8(a)ndash8(c) As expected the vertical dis-placements of all models increased with the increase of windspeed for lower wind speeds of up to 30ms for CM1 atθ 0deg and CM2 at θ 30deg and up to 45ms for CM1 atθ 15deg the vertical response for the 05D cable models wasconsistent with the response of the 10D cable modelshowever a sudden decrease in amplitude was noticed for themodels with 05D ice accretion at 45ms for CM1 atθ 0deg and at 6ms for at CM1 at θ 15deg and CM2 at θ 30degrespectively ampe cable models with 10D encounter a smalldecay in amplitudes at low wind speeds of 45ms for CM2 at

(a) (b)

Figure 3 Bridge cable model with 10D ice accretion (a) initial foam model (b) foam and aluminium foil model

Table 1 Characteristics of the tested cable models

Cablemodel

Yaw angleα (deg)

Vertical angleβ (deg)

Relative angleθ (deg)

Ice thickness(D)

Dampingratio ()

Frequency(Hz)

Scrutonnumber

Aspectratio

CM1 0 0 0 05D and 10D 076 0395 21 46CM1 0 15 15 05D and 10D 076 0395 21 46CM2 30 15 33 05D 24 0330 51 535CM2 30 0 30 05D and 10D 24 0330 51 535CM3 60 0 60 05D 38 0290 105 92CM3 60 15 61 05D 38 0290 105 92


θ 30deg and at 75ms for CM1 at θ 15deg however for thecable model CM1 at θ 0deg a sudden increase of amplitudeswas noticed for 75ms ampe vertical vibration response forthe cables with 10D ice thickness was higher than that of thecable models with 05D ice thickness especially for windspeeds higher than 90ms

ampe mean torsional response for the cable model CM2 atθ 30deg with 05D ice accretion thickness was more consistentwith the mean torsional response of the same inclinationcable model CM2 at θ 30deg but with 10D ice accretion as itcan be noticed in Figure 9(C) however discrepancies werenoticed for the other investigated cable models For CM1 at

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Figure 5 Time history responses for CM1 θ 0deg 10(D) at 15ms (a) vertical vibration (b) torsional vibration

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tical

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Figure 8 Variation of mean vertical response with wind speed for cable models with 05D and 10D ice thickness (a) CM1 at θ 0deg (b) CM1at θ 15deg (c) CM2 at θ 30deg


θ 0deg and CM1 at θ 15deg the mean torsional response washigher for 10D ice accretion thickness when compared withthe 05D ice accretion models for all the tested wind speeds(Figures 8(a) and 8(b)) Sudden decays in amplitude werestill noticed for models with 05D ice thickness at lower windspeeds of 45ms and 6ms for the CM1 and CM2 modelsrespectively while for 10D ice thickness models the tor-sional response decay occurred at 75ms and 45ms formodels CM1 and CM2 respectively

32 Effect of Relative Angle ampe average amplitudes forvertical and torsional vibrations were investigated for dif-ferent relative angles of attack θ and it was noticed that thehighest responses corresponded to the highest relative an-gles For the cases with 05D ice accretion the cable modelsCM3 at θ 61deg and θ 60deg showed the highest vertical andtorsional responses (Figures 10(a) and 11(a)) which issimilar to the critical cases reported by Cheng et al [2] for

vertically and horizontally inclined stay cables without iceaccretion Also for relative angles of 60deg and 61deg the suddendecay of amplitude at lower wind speeds was not noticedFor the CM2 cable model both vertical and torsional re-sponses were smaller for wind speeds up to 30ms howeverfrom 45ms and up to 105ms the responses for the modelinclined at relative angle 33deg were higher than the oneregistered for the model inclined at relative angle 30deg(Figures 10(b) and 11(b))

In general for CM3 and CM2 models the torsional andvertical mean responses were higher for higher relative angleshowever by comparing the magnitude of the recorded vi-brations it can be concluded that the vibrations were con-sistent with each other for different wind speeds For theCM1 model the mean vertical response was higher forθ 0deg at higher wind speeds between 90ms and 135ms andat 6ms (Figure 10(c)) the mean torsional response howeverwas much higher for the CM1 model at θ 15deg between windspeeds of 75ms and 15ms and at 6ms (Figure 11(c))

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0180 3 6 9 12 15

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(c)

Figure 9 Variation of mean torsional response with wind speed for cable models with 05D and 10D ice thickness (a) CM1 at θ 0deg (b)CM1 at θ 15deg (c) CM2 at θ 30deg


33 Wind-Induced Response Frequency Analysis In order toobserve the variation of the response frequency under dif-ferent wind speeds Fast Fourier transform (FFT) was ap-plied for the measured vertical vibrations and the dominantfrequency for each response time history was identified ampespectral distribution obtained through the FFT analysisshowed very small frequencies without a dominant peak forwind speeds lower than 30ms for CM1 at 0deg with 05D iceaccretion and for CM2 at 30deg with 10D ice accretionfrequencies difficult to identify were noticed for wind speedslower than 45ms for models CM1 at 0deg with 10D iceaccretion and CM2 at 30deg with 05D ice accretion as rep-resented in Figures 12(a) and 12(b)

ampe frequencies of the wind-induced response werehigher for the models CM1 at 0deg and CM2 at 30deg models withhigher ice accretion (10D) having a similar trend of slightlyhigher frequencies at 105ms and at 15ms For 105mswind speed other peaks of smaller intensity were identified

in the FFT spectra around frequencies of 0025Hz and021Hz for the model CM1 at 0deg and 0025Hz for the modelCM2 at 30deg both with 10D ice accretion (Figures 13(a) and13(b)) For the 05D ice accretion the two models CM1 at0deg and CM2 at 30deg showed trends similar to each other forthe vertical response frequencies obtained at the wind speedsbetween 45ms and 15ms were (Figures 12(b)) witha slight increase at 60ms and a sudden decrease at 105msfollowed by an ascending frequency at 15ms of up to034Hz for the model CM1 at 0deg and up to 04Hz for themodel CM2 at 30deg both with 05D ice accretion A secondpeak at 018Hz was noticed only for themodel CM2 at 30deg at105ms (Figure 14(b)) while a single dominant frequencyat 03303Hz was signaled for the CM1 at 0deg model

Any changes of the frequency can indicate the change ofthe dynamic response of the cable model under the effect ofthe increasing wind speed As shown in Figures 8 and 10a sudden decrease in the frequency response is observed at

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Figure 10 Variation of mean vertical response with wind speed for cable models with 05D ice thickness (a) CM3 at θ 60deg and θ 61deg (b)CM2 at θ 30deg and θ 33deg (c) CM1 at θ 0deg and θ 15deg


45ms for the models CM1 at θ 0deg 05D CM2 at θ 30deg10D which corresponds to a low frequency point in thevertical vibration FFT shown in Figures 12(a) and 12(b) forthe same wind speed Similarly for other models such asCM1 at θ 15deg 05D and 10D and CM2 at θ 30deg 05D thesudden decrease of the vertical response occurred at 60ms(Figures 8 and 10) which correspond to a low frequencypoint as well (Figure 12)

In order to compare the frequencies for the wind-induced response recorded at different wind speeds forcable models with 05D and 10D ice accretion profiles thevariation of the Strouhal number for the aforementionedcases was investigatedampe Strouhal number was determinedas St fDeqU where f Deq and U are the frequency of thevertical response and the equivalent diameter of each cablemodel was exposed to the wind direction and the mean windspeed respectively It should be noted that the thickness ofthe ice accretion on the cable and the relative cable-winddirection angle were considered in estimating the equivalent

cable diameter Deq for the Strouhal number calculation asshown in Equation (1) Also Deq in Equation (1) is theequivalent cable diameter considering the ice thickness andrelative cable-wind direction angle Dc and hi are the cablediameter and mean thickness of the ice profile respectivelywhile θ is the relative wind-cable direction angle

Deq Dc + hi( 1113857 times cos(θ) (1)

Figure 15 shows that despite the frequency varia-tions indicated in Figure 10 the normalized frequencies(Strouhal numbers) for all the performed cases decreasedwith the increase of wind speed as expected Also Fig-ure 15 shows that for different relative wind-cable anglesthe normalized frequencies for the cases with the same icethickness were almost identical According to Hao [28]the galloping divergent vibration can occur for Strouhalnumbers lower than 005 the value corresponding to thehorizontal dashed line in Figure 15 showing the incipientconditions from which the galloping divergent vibration

0

Tors

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0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 61degCM3 (05D) θ = 60deg

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Tors

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CM1 (05D) θ = 15degCM1 (05D) θ = 0deg

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Tors

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4

35

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15

1

05

(c)

Figure 11 Variation of mean torsional response with wind speed for cable models with 05D ice thickness (a) CM3 at θ 60deg and θ 61deg (b)CM2 at θ 30deg and θ 33deg (c) CM1 at θ 0deg and θ 15deg


could occur for both cable models with 05D ice ac-cretion and with 10D ice accretion from wind tunnelwind speeds as low as 30ms

ampe critical wind speed after which galloping instabilitycan be expected for all cable models tested can be de-termined using Equation (2) [16 29] In Equation (2) Ucritf D and Sc are critical wind speed natural frequency of thefundamental mode of vibration cable diameter and theScruton number respectively

Ucrit 40fDSc

1113968 (2)

Using Equation (2) the critical wind speeds were de-termined spanned between 45ms and 105ms for themodels CM1 at θ 0deg with 05D and CM3 at θ 61deg with 10Drespectively ampese wind speeds coincide with the suddenchanges in the vertical response frequencies presented inFigures 8 and 10 showing that the higher wind-inducedresponse occurred at different wind speeds depending on

the relative angle of attack and the thickness of the ice profiletested

4 Conclusions

Cable-stayed bridges stability rely on all the structuralmembers composing these massive structures and the staycables which are the most flexible elements of the bridgeand have a significant role in the overall bridge design ampewind tunnel experiment performed for cables with ice ac-cretion reported herewith clarifies some aspects related tothe wind-induced response for the ice-accreted bridge yawedand inclined stay cables Different parameters such as thevertical inclination angle (0deg and 15deg) yaw angle (0deg 15deg 30degand 60deg) ice accretion profile thickness (05D and 10D) andwind tunnel wind speed (15 to 15ms) were consideredampeincrease of ice accretion thickness was shown to increase thewind-induced response especially for wind speeds higher

0328

0332

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Freq

uenc

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CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

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3 5 7 9 11 13 15

Freq

uenc

y (H

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Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(b)

Figure 12 Vertical vibrations frequencies for models with 05D and 10D ice accretion (a) CM1 (θ 0deg) (b) CM2 (θ 30deg)

0 01 02 03 04 050

5

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35

X 03431Y 3262

(a)

0 01 02 03 04 050

5

10

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45

X 03964Y 4195

(b)

Figure 13 FFTdistribution of frequencies for models with an ice thickness of 10D at 105ms for (a) CM1 (θ 0deg) and (b) CM2 (θ 30deg)


than 45ms Both vertical and torsional displacements in-creased with the increase of the relative angles of attackhowever the investigated angles did not determine a sig-nificant increase of the wind-induced response for the 05Dand 10D ice-accreted stay cables Also at certain windspeeds the vibration for the cables with higher inclinationangles was smaller than the cases with lower inclinationshowever for wind speeds beyond 75ms the response of thecables with higher inclination angles surpassed the case withlower inclination angles A sudden decrease in the verticalvibration occurred for models CM1 at θ 0deg 05D CM2 atθ 30deg 10D and CM2 at θ 33deg 10D for wind tunnel windspeeds of 45ms for which the frequency analysis showedlower frequency points A similar decrease in response wasnoticed at wind speeds of 60ms and above for modelsCM1 at θ 15deg 05D and 10D and CM2 at θ 30deg 05Dampefrequency analysis showed multiple vibration values for thevertical wind-induced response between wind speeds 45msand 90ms for models with 05D ice accretion and between

wind speeds of 75ms and 15ms for models with 10D iceaccretion which can be an indication of an aerodynamicinstability

Data Availability

ampe data supporting the current research project can befound at CVGDepartment University of Ottawa and can bemade available if necessary by the authors

Conflicts of Interest

ampe authors declare that they have no conflicts of interest

Acknowledgments

ampis work was supported by the Natural Sciences and En-gineering Research Council of Canada (NSERC) DiscoveryGrant 06776 2015

0 01 02 03 04 050

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CM1 (05D) θ = 0degCM2 (05D) θ = 30degCM1 (05D) θ = 15deg CM2 (10D) θ = 30deg

CM1 (10D) θ = 0degCM1 (10D) θ = 15deg

Figure 15 Normalized frequency (St fDeqU) for the vertical vibrations


References

[1] M Matsumoto H Shirato T Yagi M Goto S Sakai andJ Ohya ldquoField observation of th full-scale wind-induced cablevibrationrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 91 no 1-2 pp 13ndash26 1995

[2] S Cheng G L Larose M G Savage H Tanaka andP A Irwin ldquoExperimental study on the wind-inducedvibration of a dry inclined cableminuspart I phenomenardquo Jour-nal of Wind Engineering and Industrial Aerodynamics vol 96no 12 pp 2231ndash2253 2008

[3] M Raoof ldquoFree-bending fatigue life estimation of cables atpoints of fixityrdquo Journal of Engineering Mechanics vol 118no 9 pp 1747ndash1764 1992

[4] J Druez S Louchez and P McComber ldquoIce shedding fromcablesrdquo Cold Regions Science and Technology vol 23 no 4pp 377ndash388 1995

[5] D Zuo and N P Jones Stay-cable VibrationMonitoring of theFred Hartman Bridge (Houston Texas) and the VeteransMemorial Bridge (Port Arthur Texas) Center for Trans-portation Research Bureau of Engineering Research Uni-versity of Texas at Austin Austin TX USA 2005

[6] A Davenport ldquoBuffeting of a suspension bridge by stormwindsrdquo ASCE Journal of Structural Division vol 88 no 3pp 233ndash268 1962

[7] D H Yeo and N P Jones ldquoComputational study on 3-Daerodynamic characteristics of flow around a yawed inclinedcircular cylinderrdquo NSEL Report Series Report No NSEL-027University of Illinois at Urbana-Champaign Champaign ILUSA 2011

[8] M Matsumoto N Shiraishi and H Shirato ldquoRain-windinduced vibration of cables of cable-stayed bridgesrdquo Jour-nal of Wind Engineering and Industrial Aerodynamics vol 43no 1ndash3 pp 2011ndash2022 1992

[9] M Matsumoto T Yagi H Hatsudab T Shimac M Tanakadand H Naitoa ldquoDry galloping characteristics and its mech-anism of inclinedyawed cablesrdquo Journal of Wind Engineeringand Industrial Aerodynamics vol 98 no 6-7 pp 317ndash3272010

[10] Q Liu F Zhang M Wenyong and W Yi ldquoExperimentalstudy on Reynolds number effect on dry cable galloping ofstay cablesrdquo in Proceedings of the 13th International Con-ference on Wind Engineering Amsterdam Netherlands July2011

[11] J H G Macdonald and G L Larose ldquoA unified approach toaerodynamic damping and draglift instabilities and its ap-plication to dry inclined cable gallopingrdquo Journal of Fluidsand Structures vol 22 no 2 pp 229ndash252 2006

[12] M S Hoftyzer and E Dragomirescu ldquoNumerical in-vestigation of flow behaviour around inclined circular cyl-indersrdquo in Proceedings of the Fifth International Symposiumon ComputationalWind Engineering (CWE2010) Chapel HillNC USA May 2010

[13] M Matsumoto Y Shigemura Y Daito and T KanamuraldquoHigh speed vortex shedding vibration of inclined cablesrdquo inProceedings of the Second International Symposium on CableDynamics pp 27ndash35 Tokyo Japan October 1997

[14] W Martin E Naudascher and I Currie ldquoStreamwise os-cillations of cylindersrdquo Journal of the Engineering MechanicsDivision vol 107 pp 589ndash607 1981

[15] H Tabatabai Inspection andMaintenance of Bridge Stay CableSystems NCHRP Synthesis 353 National Cooperative Re-search Program Transportation Research Board 2005

[16] S Kumarasena N P Jones P Irwin and P Taylor Wind-Induced Vibration of Stay Cables US Department of Trans-portation Federal Highway Association Publication NoFHWA-RD-05-083 Washington DC USA 2007

[17] NJ Gimsing and CT Georgakis Cable Supported BridgesConcept and Design Wiley Chichester England 2011

[18] P McComber and A Paradis ldquoA cable galloping model forthin ice accretionsrdquo Atmospheric Research vol 46 no 1-2pp 13ndash25 1998

[19] C Demartino H H Koss C T Georgakis and F RicciardellildquoEffects of ice accretion on the aerodynamics of bridge cablesrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 138 pp 98ndash119 2015

[20] H Gjelstrup C T Georgakis and A Larsen ldquoAn evaluationof iced bridge hanger vibrations through wind tunnel testingand quasi-steady theoryrdquo Wind and Structures An In-ternational Journal vol 15 no 5 pp 385ndash407 2012

[21] L J Vincentsen and P Lundhus e Oslashresund and the GreatBelt linksmdashExperience and Developments IABSE Sympo-siumWeimar Germany 2007

[22] H H Koss and G Matteoni ldquoExperimental investigation ofaerodynamic loads on iced cylindersrdquo in Proceedings of 9thInternational Symposium on Cable Dynamics ShanghaiOctober 2011

[23] H H Koss H Gjelstrup and C T Georgakis ldquoExperimentalstudy of ice accretion on circular cylinders at moderate lowtemperaturesrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 104ndash106 pp 540ndash546 2012

[24] H H Koss and M S M Lund ldquoExperimental investigation ofaerodynamic instability of iced bridge sectionsrdquo in Pro-ceedings of 6th European and African Conference on WindEngineering Robinson College Cambridge UK July 2013

[25] H H Koss J F Henningsen and I Olsenn ldquoInfluence oficing on bridge cable aerodynamicsrdquo in Proceedings of Fif-teenth International Workshop on Atmospheric Icing ofStructures StJohnrsquos Newfoundland and Labrador CanadaSeptember 2013

[26] C Demartino and F Ricciardelli ldquoAerodynamic stability ofice-accreted bridge cablesrdquo Journal of Fluids and Structuresvol 52 pp 81ndash100 2015

[27] G S West and C J Apelt ldquoampe effects of tunnel blockage andaspect ratio on the mean flow past a circular cylinder withReynolds numbers between 104 and 105rdquo Journal of FluidMechanics vol 114 no 1 pp 361ndash377 1982

[28] H Hao ldquoampe galloping phenomenon and its control ofbridgesrdquo Masterrsquos thesis Changrsquoan University Xirsquoan China2010 in Chinese

[29] T Saito M Matsumoto and M Kitazawa ldquoRain-wind ex-citation of cables on cable- stayed Higashi-Kobe bridge andcable vibration controlrdquo in Proceedings of the InternationalConference on Cable-Stayed and Suspension Bridgespp 507ndash514 AFPC Deauville France 1994


International Journal of

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Shock and Vibration


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Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

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Hindawi

wwwhindawicom Volume 2018

Advances in

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Submit your manuscripts atwwwhindawicom

In an attempt to clarify the onset conditions for the ice-accreted cable vibrations Koss andMatteoni [22] conducteda wind tunnel experiment for determining the effect of iceaccretion on the aerodynamic forces recorded for full-scalecables under 0deg angle of attack and Re numbers of up to32times105 using the FORCEDTU climatic wind tunnel(CWT) Also Koss et al [23] performed an experimentalinvestigation for determining the shape of the ice accretionformed on cables of 00381m and 0089m in diameter thatwere oriented in horizontal and vertical directions fordifferent exposure times and air temperatures ampey clas-sified the regions of the ice accretion profiles into the corecenter area outer area flow-out flow-out accumulation andrunback ampe effect of the ice accretion on the aerodynamicsof the vertical bridge hangers was investigated by Gjelstrupet al [20] using static and dynamic wind tunnel tests ampeaerodynamic coefficients were determined for smooth andrough surfaces of the ice-accreted cables under smooth andturbulent wind flow conditions Furthermore Koss andLund [24] presented the results of a full-scale experimentalstudy on horizontal 160mm diameter bridge cables underwet and dry ice accretion conditions using an innovativespray system to determine the aerodynamic coefficients andto evaluate the galloping instability using the Den Hartogcriterion Moreover Koss et al [25] studied the formation ofice accretion on three full-scale horizontal bridge cables withplain helical fillet and indented high density polyethylene(HDPE) cover under wet and dry climatic conditions andthey concluded that gravity plays a major role in the iceprofile formation on the cables under the wet icing con-dition Also this study indicated that only the cable withplain HDPE cover was susceptible to galloping instability asper the Den Hartog criterion Demartino et al [19] extendedthis study to full-scale HDPE vertical and inclined bridgecables and they investigated the process of ice accretionformation the final ice shape and the correspondingaerodynamic drag lift and moment coefficients for differentparameters such as temperature wind speed and yaw angleUsing the experimental data of Demartino et al [19]Demartino and Ricciardelli [26] modelled different gallop-ing vibrations for one degree of freedom (1-DOF) andmultiple degrees of freedom (MDOF) cables and they an-alyzed the stability of bridge cables with ice accretion Re-sults showed that the 1-DOF models usually generateconservative results and the use of dynamic wind tunnelexperiments was recommended to confirm the results ofexisting theoretical models especially for the cases where nosufficient data are available

However the actual wind-induced vibrations for theinclined and yawed cables in regard to the wind directionwhich are very often encountered in practise with ice ac-cretion attached to their surface were not specifically in-vestigated ampe current study examines the aerodynamicbehavior of yawed and inclined ice-accreted stay cables ampestay cable models had vertical inclination angles of 0deg and 15degand yaw angles of 0deg 15deg 30deg and 60deg while the ice accretionprofile thickness were 05D and 10D Wind tunnel windspeeds between 15ms and 15ms were considered toidentify the critical wind-induced cable vibrations

2 Experimental Set-Up and CableModel Configuration

ampeexperimental programwas performed in the suction windtunnel facility of the University of Ottawa Department ofMechanical Engineering (Figure 1(a)) which has a testingsection of 61 cmtimes 92 cm and has three openings on each sideof the testing section used for installing the models and tocoordinate the necessary vertical and yaw inclination anglesfor the cable models ampe maximumwind speed which can beachieved in the wind tunnel is 300ms however for thecurrent experiment the ice-accreted cable was tested for windspeeds of up to 150ms corresponding to a Reynolds numberof 40times105 considering the high amplitude vibrations de-veloped beyond these testing conditions ampe wind speedvaried during the tests from 15ms to 150ms in steps of15msampe blockage ratio was determined as the total area ofthe model normal to the free stream velocity divided by thetotal area of the test section and was found to be 0368times10minus3and 0736times10minus3 for the cable models with 10 cm and 20 cmice profiles respectively According to West and Apelt [27] ifthe blockage ratio is lower than 6 for smooth cylinders withaspect ratios in the range of 4 to 10 the Strouhal number isnot affected and no correction is needed for the aerodynamiccoefficients hence the turbulence intensity would not bea significant concern

An important parameter which can significantly affect thewind-induced response of the cable models during the windtunnel tests is the relative angle of attack between the winddirection and the cable axisamperefore the wind-cable relativeangle as defined by Cheng et al [2] was employed in thecurrent research that is θ cosminus1(cosα cos β) where θ αand β represent the relative wind-cable angle yaw andvertical cable inclination angles respectively (Figure 1(b)) Tosimulate the wind-induced vibrations of the cables eightsupporting springs each of elastic constant k 15Nm wereinstalled symmetrically at the two ends of the cables along thevertical direction as schematically represented in Figure 1(b)Also the position of the cable models was adjusted using thethree circular openings in the wind tunnel lateral wall and bymoving the entire spring support system installed outside thetunnel to adjust for different vertical and yaw angles of attackas shown in Figures 2(a) and 2(b) For flow perpendicular tothe cylinder at 0deg yaw the same location openings were usedfor installing themodel (Figure 2(c)) while for bigger yaw andvertical angles the cable model was installed between themiddle and the last opening with an elevation differencebetween the spring support systems (Figure 2(d))

ampe cable models were scaled to 1 45 from the prototypebridge cable used by Cheng et al [2] for the full-scale windtunnel experiments conducted for the smooth surface in-clined and yawed cylinders Ice accretion profiles witha thickness of 05D and 1D where D is the diameter of thecable model were added on one side of the cable modelsampese dimensions correspond respectively to a cable iceaccretion thickness of 45 cm (05D) and 90 cm (1D) con-sidering the 1 45 scale factor According to Koss et al [23]exposing the cable for 1800 seconds to precipitations underfreezing conditions the ice accretion profile thickness can




(a)

α

β

θ

Wind speed

direction

Displacementsensors

Cable model

Longitudinal bar

Transverse bar

Ice accretionmodel

(b)


β

(a)

α

(b)

(c) (d)








(a) (b)



Cablemodel

Yaw angleα (deg)



Ice thickness(D)

Dampingratio ()

Frequency(Hz)

Scrutonnumber

Aspectratio





ndash40

ndash20

0

20

40

0 10 20 30 40Time (s)

Disp

lace

men

t (m

m)

(a)

ndash8

ndash4

0

4

8

0 10 20 30 40Time (s)

Deg

ree (

deg)

(b)


ndash30

ndash20

ndash10

0

10

20

30

Disp

lace

men

t (m

m)

0 20 40 60Time (s)

(a)

ndash4

ndash2

0

2

4

6

Deg

ree (

deg)

0 20 40 60Time (s)

(b)


ndash40

ndash20

0

20

40

0 5 10 15 20 25 30Time (s)

Disp

lace

men

t (m

m)

(a)

ndash3

ndash2

ndash1

0

1

2

3

0 5 10 15 20 25 30Time (s)

Deg

rees

(deg)

(b)



ndash40

ndash20

0

20

40

0 10 20 30 40

Disp

lace

men

t (m

m)

Time (s)

(a)

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

0 10 20 30 40

Deg

ree (

deg)

Time (s)

(b)


0

4

8

12

16

20

0 3 6 9 12 15 18

Ver

tical

disp

lace

men

t (m

m)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0

4

8

12

16

20

24V

ertic

al d

ispla

cem

ent (

mm

)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (10D) θ = 15deg

(b)

0

4

8

12

16

20

24

0 3 6 9 12 15 18

Ver

tical

disp

lace

men

t (m

m)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(c)







Tors

ion

(deg)

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

Tors

ion

(deg)

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM1 (05D) θ = 15degCM1 (10D) θ = 15deg

(b)

Tors

ion

(deg)

35

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(c)







0

Vert

ical

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 60degCM3 (05D) θ = 61deg

(a)

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 0degCM1 (05D) θ = 15deg

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

(c)








0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 61degCM3 (05D) θ = 60deg

(a)

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (05D) θ = 0deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(c)





Ucrit 40fDSc

1113968 (2)



4 Conclusions


0328

0332

0336

034

0344

0348

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0386

0388

039

0392

0394

0396

0398

04

0402

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(b)


0 01 02 03 04 050

5

10

15

20

25

30

35

X 03431Y 3262

(a)

0 01 02 03 04 050

5

10

15

20

25

30

35

40

45

X 03964Y 4195

(b)





Data Availability




Acknowledgments


0 01 02 03 04 050

5

10

15

20

25

X 03303Y 2274

(a)

0 01 02 03 04 050

10

20

30

40

50

60X 03937Y 587

(b)


0005

0015

0025

0035

0045

0055

0065

0075

0085

0 2 4 6 8 10 12 14 16

St=fD

eqU

Wind speed (ms)


CM1 (10D) θ = 0degCM1 (10D) θ = 15deg



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




(a)

α

β

θ

Wind speed

direction

Displacementsensors

Cable model

Longitudinal bar

Transverse bar

Ice accretionmodel

(b)


β

(a)

α

(b)

(c) (d)








(a) (b)



Cablemodel

Yaw angleα (deg)



Ice thickness(D)

Dampingratio ()

Frequency(Hz)

Scrutonnumber

Aspectratio





ndash40

ndash20

0

20

40

0 10 20 30 40Time (s)

Disp

lace

men

t (m

m)

(a)

ndash8

ndash4

0

4

8

0 10 20 30 40Time (s)

Deg

ree (

deg)

(b)


ndash30

ndash20

ndash10

0

10

20

30

Disp

lace

men

t (m

m)

0 20 40 60Time (s)

(a)

ndash4

ndash2

0

2

4

6

Deg

ree (

deg)

0 20 40 60Time (s)

(b)


ndash40

ndash20

0

20

40

0 5 10 15 20 25 30Time (s)

Disp

lace

men

t (m

m)

(a)

ndash3

ndash2

ndash1

0

1

2

3

0 5 10 15 20 25 30Time (s)

Deg

rees

(deg)

(b)



ndash40

ndash20

0

20

40

0 10 20 30 40

Disp

lace

men

t (m

m)

Time (s)

(a)

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

0 10 20 30 40

Deg

ree (

deg)

Time (s)

(b)


0

4

8

12

16

20

0 3 6 9 12 15 18

Ver

tical

disp

lace

men

t (m

m)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0

4

8

12

16

20

24V

ertic

al d

ispla

cem

ent (

mm

)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (10D) θ = 15deg

(b)

0

4

8

12

16

20

24

0 3 6 9 12 15 18

Ver

tical

disp

lace

men

t (m

m)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(c)







Tors

ion

(deg)

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

Tors

ion

(deg)

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM1 (05D) θ = 15degCM1 (10D) θ = 15deg

(b)

Tors

ion

(deg)

35

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(c)







0

Vert

ical

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 60degCM3 (05D) θ = 61deg

(a)

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 0degCM1 (05D) θ = 15deg

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

(c)








0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 61degCM3 (05D) θ = 60deg

(a)

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (05D) θ = 0deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(c)





Ucrit 40fDSc

1113968 (2)



4 Conclusions


0328

0332

0336

034

0344

0348

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0386

0388

039

0392

0394

0396

0398

04

0402

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(b)


0 01 02 03 04 050

5

10

15

20

25

30

35

X 03431Y 3262

(a)

0 01 02 03 04 050

5

10

15

20

25

30

35

40

45

X 03964Y 4195

(b)





Data Availability




Acknowledgments


0 01 02 03 04 050

5

10

15

20

25

X 03303Y 2274

(a)

0 01 02 03 04 050

10

20

30

40

50

60X 03937Y 587

(b)


0005

0015

0025

0035

0045

0055

0065

0075

0085

0 2 4 6 8 10 12 14 16

St=fD

eqU

Wind speed (ms)


CM1 (10D) θ = 0degCM1 (10D) θ = 15deg



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







(a) (b)



Cablemodel

Yaw angleα (deg)



Ice thickness(D)

Dampingratio ()

Frequency(Hz)

Scrutonnumber

Aspectratio





ndash40

ndash20

0

20

40

0 10 20 30 40Time (s)

Disp

lace

men

t (m

m)

(a)

ndash8

ndash4

0

4

8

0 10 20 30 40Time (s)

Deg

ree (

deg)

(b)


ndash30

ndash20

ndash10

0

10

20

30

Disp

lace

men

t (m

m)

0 20 40 60Time (s)

(a)

ndash4

ndash2

0

2

4

6

Deg

ree (

deg)

0 20 40 60Time (s)

(b)


ndash40

ndash20

0

20

40

0 5 10 15 20 25 30Time (s)

Disp

lace

men

t (m

m)

(a)

ndash3

ndash2

ndash1

0

1

2

3

0 5 10 15 20 25 30Time (s)

Deg

rees

(deg)

(b)



ndash40

ndash20

0

20

40

0 10 20 30 40

Disp

lace

men

t (m

m)

Time (s)

(a)

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

0 10 20 30 40

Deg

ree (

deg)

Time (s)

(b)


0

4

8

12

16

20

0 3 6 9 12 15 18

Ver

tical

disp

lace

men

t (m

m)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0

4

8

12

16

20

24V

ertic

al d

ispla

cem

ent (

mm

)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (10D) θ = 15deg

(b)

0

4

8

12

16

20

24

0 3 6 9 12 15 18

Ver

tical

disp

lace

men

t (m

m)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(c)







Tors

ion

(deg)

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

Tors

ion

(deg)

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM1 (05D) θ = 15degCM1 (10D) θ = 15deg

(b)

Tors

ion

(deg)

35

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(c)







0

Vert

ical

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 60degCM3 (05D) θ = 61deg

(a)

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 0degCM1 (05D) θ = 15deg

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

(c)








0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 61degCM3 (05D) θ = 60deg

(a)

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (05D) θ = 0deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(c)





Ucrit 40fDSc

1113968 (2)



4 Conclusions


0328

0332

0336

034

0344

0348

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0386

0388

039

0392

0394

0396

0398

04

0402

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(b)


0 01 02 03 04 050

5

10

15

20

25

30

35

X 03431Y 3262

(a)

0 01 02 03 04 050

5

10

15

20

25

30

35

40

45

X 03964Y 4195

(b)





Data Availability




Acknowledgments


0 01 02 03 04 050

5

10

15

20

25

X 03303Y 2274

(a)

0 01 02 03 04 050

10

20

30

40

50

60X 03937Y 587

(b)


0005

0015

0025

0035

0045

0055

0065

0075

0085

0 2 4 6 8 10 12 14 16

St=fD

eqU

Wind speed (ms)


CM1 (10D) θ = 0degCM1 (10D) θ = 15deg



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




ndash40

ndash20

0

20

40

0 10 20 30 40Time (s)

Disp

lace

men

t (m

m)

(a)

ndash8

ndash4

0

4

8

0 10 20 30 40Time (s)

Deg

ree (

deg)

(b)


ndash30

ndash20

ndash10

0

10

20

30

Disp

lace

men

t (m

m)

0 20 40 60Time (s)

(a)

ndash4

ndash2

0

2

4

6

Deg

ree (

deg)

0 20 40 60Time (s)

(b)


ndash40

ndash20

0

20

40

0 5 10 15 20 25 30Time (s)

Disp

lace

men

t (m

m)

(a)

ndash3

ndash2

ndash1

0

1

2

3

0 5 10 15 20 25 30Time (s)

Deg

rees

(deg)

(b)



ndash40

ndash20

0

20

40

0 10 20 30 40

Disp

lace

men

t (m

m)

Time (s)

(a)

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

0 10 20 30 40

Deg

ree (

deg)

Time (s)

(b)


0

4

8

12

16

20

0 3 6 9 12 15 18

Ver

tical

disp

lace

men

t (m

m)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0

4

8

12

16

20

24V

ertic

al d

ispla

cem

ent (

mm

)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (10D) θ = 15deg

(b)

0

4

8

12

16

20

24

0 3 6 9 12 15 18

Ver

tical

disp

lace

men

t (m

m)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(c)







Tors

ion

(deg)

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

Tors

ion

(deg)

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM1 (05D) θ = 15degCM1 (10D) θ = 15deg

(b)

Tors

ion

(deg)

35

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(c)







0

Vert

ical

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 60degCM3 (05D) θ = 61deg

(a)

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 0degCM1 (05D) θ = 15deg

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

(c)








0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 61degCM3 (05D) θ = 60deg

(a)

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (05D) θ = 0deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(c)





Ucrit 40fDSc

1113968 (2)



4 Conclusions


0328

0332

0336

034

0344

0348

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0386

0388

039

0392

0394

0396

0398

04

0402

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(b)


0 01 02 03 04 050

5

10

15

20

25

30

35

X 03431Y 3262

(a)

0 01 02 03 04 050

5

10

15

20

25

30

35

40

45

X 03964Y 4195

(b)





Data Availability




Acknowledgments


0 01 02 03 04 050

5

10

15

20

25

X 03303Y 2274

(a)

0 01 02 03 04 050

10

20

30

40

50

60X 03937Y 587

(b)


0005

0015

0025

0035

0045

0055

0065

0075

0085

0 2 4 6 8 10 12 14 16

St=fD

eqU

Wind speed (ms)


CM1 (10D) θ = 0degCM1 (10D) θ = 15deg



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


ndash40

ndash20

0

20

40

0 10 20 30 40

Disp

lace

men

t (m

m)

Time (s)

(a)

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

0 10 20 30 40

Deg

ree (

deg)

Time (s)

(b)


0

4

8

12

16

20

0 3 6 9 12 15 18

Ver

tical

disp

lace

men

t (m

m)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0

4

8

12

16

20

24V

ertic

al d

ispla

cem

ent (

mm

)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (10D) θ = 15deg

(b)

0

4

8

12

16

20

24

0 3 6 9 12 15 18

Ver

tical

disp

lace

men

t (m

m)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(c)







Tors

ion

(deg)

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

Tors

ion

(deg)

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM1 (05D) θ = 15degCM1 (10D) θ = 15deg

(b)

Tors

ion

(deg)

35

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(c)







0

Vert

ical

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 60degCM3 (05D) θ = 61deg

(a)

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 0degCM1 (05D) θ = 15deg

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

(c)








0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 61degCM3 (05D) θ = 60deg

(a)

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (05D) θ = 0deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(c)





Ucrit 40fDSc

1113968 (2)



4 Conclusions


0328

0332

0336

034

0344

0348

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0386

0388

039

0392

0394

0396

0398

04

0402

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(b)


0 01 02 03 04 050

5

10

15

20

25

30

35

X 03431Y 3262

(a)

0 01 02 03 04 050

5

10

15

20

25

30

35

40

45

X 03964Y 4195

(b)





Data Availability




Acknowledgments


0 01 02 03 04 050

5

10

15

20

25

X 03303Y 2274

(a)

0 01 02 03 04 050

10

20

30

40

50

60X 03937Y 587

(b)


0005

0015

0025

0035

0045

0055

0065

0075

0085

0 2 4 6 8 10 12 14 16

St=fD

eqU

Wind speed (ms)


CM1 (10D) θ = 0degCM1 (10D) θ = 15deg



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Tors

ion

(deg)

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

Tors

ion

(deg)

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM1 (05D) θ = 15degCM1 (10D) θ = 15deg

(b)

Tors

ion

(deg)

35

3

25

2

15

1

05

0180 3 6 9 12 15

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(c)







0

Vert

ical

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 60degCM3 (05D) θ = 61deg

(a)

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 0degCM1 (05D) θ = 15deg

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

(c)








0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 61degCM3 (05D) θ = 60deg

(a)

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (05D) θ = 0deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(c)





Ucrit 40fDSc

1113968 (2)



4 Conclusions


0328

0332

0336

034

0344

0348

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0386

0388

039

0392

0394

0396

0398

04

0402

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(b)


0 01 02 03 04 050

5

10

15

20

25

30

35

X 03431Y 3262

(a)

0 01 02 03 04 050

5

10

15

20

25

30

35

40

45

X 03964Y 4195

(b)





Data Availability




Acknowledgments


0 01 02 03 04 050

5

10

15

20

25

X 03303Y 2274

(a)

0 01 02 03 04 050

10

20

30

40

50

60X 03937Y 587

(b)


0005

0015

0025

0035

0045

0055

0065

0075

0085

0 2 4 6 8 10 12 14 16

St=fD

eqU

Wind speed (ms)


CM1 (10D) θ = 0degCM1 (10D) θ = 15deg



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






0

Vert

ical

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 60degCM3 (05D) θ = 61deg

(a)

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 0degCM1 (05D) θ = 15deg

0

Vert

cial

disp

lace

men

t (m

m)

25

20

15

10

5

(c)








0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 61degCM3 (05D) θ = 60deg

(a)

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (05D) θ = 0deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(c)





Ucrit 40fDSc

1113968 (2)



4 Conclusions


0328

0332

0336

034

0344

0348

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0386

0388

039

0392

0394

0396

0398

04

0402

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(b)


0 01 02 03 04 050

5

10

15

20

25

30

35

X 03431Y 3262

(a)

0 01 02 03 04 050

5

10

15

20

25

30

35

40

45

X 03964Y 4195

(b)





Data Availability




Acknowledgments


0 01 02 03 04 050

5

10

15

20

25

X 03303Y 2274

(a)

0 01 02 03 04 050

10

20

30

40

50

60X 03937Y 587

(b)


0005

0015

0025

0035

0045

0055

0065

0075

0085

0 2 4 6 8 10 12 14 16

St=fD

eqU

Wind speed (ms)


CM1 (10D) θ = 0degCM1 (10D) θ = 15deg



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

0 3 6 9 12 15 18Wind speed (ms)

CM3 (05D) θ = 61degCM3 (05D) θ = 60deg

(a)

0 3 6 9 12 15 18Wind speed (ms)

CM2 (05D) θ = 33degCM2 (05D) θ = 30deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(b)

0 3 6 9 12 15 18Wind speed (ms)

CM1 (05D) θ = 15degCM1 (05D) θ = 0deg

0

Tors

ion

(deg)

4

35

3

25

2

15

1

05

(c)





Ucrit 40fDSc

1113968 (2)



4 Conclusions


0328

0332

0336

034

0344

0348

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0386

0388

039

0392

0394

0396

0398

04

0402

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(b)


0 01 02 03 04 050

5

10

15

20

25

30

35

X 03431Y 3262

(a)

0 01 02 03 04 050

5

10

15

20

25

30

35

40

45

X 03964Y 4195

(b)





Data Availability




Acknowledgments


0 01 02 03 04 050

5

10

15

20

25

X 03303Y 2274

(a)

0 01 02 03 04 050

10

20

30

40

50

60X 03937Y 587

(b)


0005

0015

0025

0035

0045

0055

0065

0075

0085

0 2 4 6 8 10 12 14 16

St=fD

eqU

Wind speed (ms)


CM1 (10D) θ = 0degCM1 (10D) θ = 15deg



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Ucrit 40fDSc

1113968 (2)



4 Conclusions


0328

0332

0336

034

0344

0348

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM1 (05D) θ = 0degCM1 (10D) θ = 0deg

(a)

0386

0388

039

0392

0394

0396

0398

04

0402

3 5 7 9 11 13 15

Freq

uenc

y (H

z)

Wind speed (ms)

CM2 (05D) θ = 30degCM2 (10D) θ = 30deg

(b)


0 01 02 03 04 050

5

10

15

20

25

30

35

X 03431Y 3262

(a)

0 01 02 03 04 050

5

10

15

20

25

30

35

40

45

X 03964Y 4195

(b)





Data Availability




Acknowledgments


0 01 02 03 04 050

5

10

15

20

25

X 03303Y 2274

(a)

0 01 02 03 04 050

10

20

30

40

50

60X 03937Y 587

(b)


0005

0015

0025

0035

0045

0055

0065

0075

0085

0 2 4 6 8 10 12 14 16

St=fD

eqU

Wind speed (ms)


CM1 (10D) θ = 0degCM1 (10D) θ = 15deg



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability




Acknowledgments


0 01 02 03 04 050

5

10

15

20

25

X 03303Y 2274

(a)

0 01 02 03 04 050

10

20

30

40

50

60X 03937Y 587

(b)


0005

0015

0025

0035

0045

0055

0065

0075

0085

0 2 4 6 8 10 12 14 16

St=fD

eqU

Wind speed (ms)


CM1 (10D) θ = 0degCM1 (10D) θ = 15deg



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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