Wind tunnel demonstration of galloping mitigation with a purely nonlinear energy sink Michael M. Selwanis, Guilherme Rosa Franzini,Cédric Béguin, Frédérick P. Gosselin Highlights Wind tunnel demonstration of galloping mitigation with a purely nonlinear energy sink Michael M. Selwanis, Guilherme Rosa Franzini,Cédric Béguin, Frédérick P. Gosselin •AfreeballinacirculartrackactsasaNon-linearEnergySink(NES)anddelaystheoccurrenceofgallopingto higher ﬂow speeds. •The proposed NES design is robust and works over a large parameter range. •TherotativeNESexperiencesthreesuccessiveresponsemodeswithincreasingﬂowvelocity;oscillatoryregime, intermittent regime, and rotational regime. •Theballmass,trackradius,balldamping,andradialclearancebetweentheballandtheNEStrackarethemain NES parameters and have a signiﬁcant eﬀect on its behaviour. Wind tunnel demonstration of galloping mitigation with a purely nonlinear energy sink Michael M. Selwanisa,b,<, Guilherme Rosa Franzinic, Cédric Béguinaand Frédérick P. Gosselina,<< aDepartment of Mechanical Engineering, Polytechnique Montréal , Québec, Canada bAerospace Engineering Department, Military Technical College, Cairo, Egypt cOﬀshore Mechanics Laboratory, Escola Politécnica, University of São Paulo, Brazil ARTICLE INFO Keywords : Non-linear energy sink Vibration suppression Square prism Galloping Energy transfer Wind tunnel testsABSTRACT Gallopingisacriticaltypeofﬂow-inducedvibration(FIV)arisingonpowertransmissionlines, highrisebuildings,pipeandcablesbundlesintheoilandgasindustry. Inthispaper,wepresent apurelynonlinearenergysink(NES)thatmitigatesthegallopingofasquareprism. TheNESis composed of a ball rotating freely in a circular track attached to the prism. The ball’s dynamics is coupled to that of the prism in a purely nonlinear way by inertia. We experimentally assess how this simple NES reduces the prism vibration by comparing the prism amplitude responses withandwithouttheNES.Asupplementaryvideopresentstheseexperiments,duringwhichthe NES ball exhibits diﬀerent dynamics in three regimes; oscillatory, intermittent, and rotational. We characterize the ball behaviour and its eﬀect on the prism response in each regime. The oscillatory regime appears at low ﬂow speeds at which both the prism and the ball oscillate withsmallamplitude. Theintermittentregimerepresentsatransitionmodewithinasmallrange of ﬂow speeds and corresponds to a small jump in the vibration amplitude of the prism. The rotational regime appears at higher ﬂow speeds, where the ball oscillates with relatively high angular speeds resulting in a strong modulated response of the prism. The design of the NES allowstoeasilyvaryitstrackdimensionstouseaballofdiﬀerentsizesandmasses. Accordingly, we demonstrate the inﬂuence of the main NES parameters, which are the ball mass, NES track radius,ballfriction,andradialclearancebetweenNEStrackwallsandtherotatingball,onboth theprismresponseandtheballbehaviour. TheNESwepresentisdirectlyamenabletomitigate other types of FIV. 1. Introduction Transverse galloping is a critical type of ﬂow-induced vibration (FIV) that commonly occurs at high ﬂow speeds. Duringheavywind,gallopingmayhavedestructiveeﬀectsonmanystructuressuchasskyscrapers,transmissionlines, and road signs. A linear Tuned Mass Damper (TMD) is a simple device used for damping vibration of structures. This mass-spring-damper system (Hijmissen and van Horssen, 2007) is tuned to change the natural frequency of the system. ATMDworkseﬃcientlyinanarrowfrequencybandbutaddsnewpotentialresonancestothemainstructure. Contrary to the TMD, another particular class of suppressors known as nonlinear energy sinks (NES) have no linear naturalfrequency(Leeetal.,2008)andcanengagewiththeprimaryvibratingsystemsoverabroadrangeoffrequencies reducing its vibration amplitude. A NES is a passive vibration suppressor that consists of a mass added to a primary structure and characterized by anon-linearizablestiﬀnessandusuallylineardampingproperties(Leeetal.,2008). ANESwithoutdirectattachment totheprimarystructure(Pennisietal.,2017;Lietal.,2018)isaspecialtypeofsuchdeviceswithzero-stiﬀness,their dynamics is purely nonlinear. A NES works by Targeted Energy Transfer (TET) (Vakakis et al., 2008; Gendelman, 2008): during vibration, a portion of the energy is transferred irreversibly from the primary structure to the NES reducing vibration amplitudes. The great interest in the ﬁeld of nonlinear energy absorption has led to various NES designs. In a vibro-impact NES, the impacts of balls with rigid walls dissipate energy (Gendelman and Alloni, 2015). In a translative NES, a smallmassattachedtothemainstructurebyanessentiallynon-linearspringandadashpotabsorbsvibrationduringits <Corresponding author; email address (michael.selwanis@polymtl.ca) <<Principal corresponding author; email address (frederick.gosselin@polymtl.ca) ORCID(s): Michael M. Selwanis et al.: Preprint submitted to Elsevier Page 1 of 14 Wind tunnel demonstration of galloping mitigation with a ball energy sink Nomenclature Logarithmic decrement, = 2yfor lightly damped systems Radial clearance between the NES ball and the track side walls, =wt*2rb !Natural angular frequency, =ù k_m Ball angular coordinates relative to the prism AVibration amplitude cSystem damping coeﬃcient cBall damping coeﬃcient DSide length of the square prism cross section fnNatural frequency, =!_2 fvsVortex shedding frequency kSpring stiﬀness LHeight of the square prism MTotal oscillating mass mbNES ball mass rNES track mean radius rbNES ball radiusStStrouhal number ttime UFlow stream velocity UrReduced ﬂow velocity, =U_!D UcCritical ﬂow speed Ulock*inLock-in ﬂow speed, =fvsD_St wtNES track width yDisplacement normal to the ﬂow direction Non-dimensional parameters  NES relative clearance, =_rb ANon-dimensional vibration amplitude, =A_D  mNES mass ratio, =mb_M+mb  rNES radius ratio, =r_D YNon-dimensional vibration displacement, =y_D Onset velocity ratio, =Ug_Uvs Ball damping ratio, =c_2mbr2! ySystem damping ratio, =c_2.M+mb/! translationalmotion(Dongyangetal.,2018;Guoetal.,2017). WhileinarotativeNES(Saeedetal.,2019),arotating rigid bar with a tip-mass attached to the main structure represents another technique for vibration suppression. The rotative NES is a simple and promising device that can damp vibration without a spring element (Ueno and Franzini, 2019). Only a few contributions are concerned with the passive suppression of galloping by a NES. Dai et al. (2016) analytically and numerically studied the response of a square prism ﬁtted with a translative NES. This study pointed outtheinﬂuenceoftheNESparametersontheonsetofthecriticalgallopingvelocity,aswellasthestronglymodulated responsesoftheprism. Teixeiraetal.(2018)addressedasimilarproblemwithconsideringarotativeNES.Throughout the numerical simulations, the NES can reduce the vibration amplitudes of the prism to half its original values. However,inthelastdecade,researchershaveusedvariousNESdesignstosuppressaparticulartypeofFIVdiﬀerent from galopping, e.g., vortex-induced vibrations (VIV). Tumkur et al. (2013) investigated the dynamics of a cylinder ﬁttedwithatranslativeNESusingComputationalFluidsDynamics(CFD)andreporteda75%reductioninthecylinder vibrationamplitudesduetovortexshedding. AsimilarapproachwasemployedbyMehmoodetal.(2014),whopointed out the dependence of the suppression eﬃciency with the initial conditions. Blanchard et al. (2020) focused on VIV suppression using a rotative NES. The authors used CFD approaches for computing the ﬂuid loads and highlighted the signiﬁcant energy transfer that appears in the strongly modulated responses of the cylinder. Conversely, Dai et al. (2017) employed the wake-oscillator models for evaluating the ﬂuid forces due to VIV and showed that a translative NEScansimilarlymodulatethecylinderresponses. UenoandFranzini(2019)studiedtheeﬀectoftheNESparameters on the oscillation amplitude of the cylinder. Experimental investigations related to NESs are fewer than theoretical ones and mostly deal with the NES as a passive suppressor for building vibration. Wierschem et al. (2012) tested a 2-DOF NES to damp impulsive excitation showing a good eﬀect for TET on improving the structural damping. In a similar study (AL-Shudeifat et al., 2013), a vibro-impact NES highly enhanced the damping properties of a structure. Wang et al. (2016) examined a diﬀerent vibro-impact NES showing its eﬀect on mitigating impulsive and seismic excitation. Wierschem et al. (2017) used a system of NESs to reduce the structural vibrations generated from transient loads due to blast testing of a large scale steel structure. IntermsofmitigatingFIVwithaNES,fewexperimentsareavailableintheliterature. Dongyangetal.(2018);Dai Michael M. Selwanis et al.: Preprint submitted to Elsevier Page 2 of 14 Wind tunnel demonstration of galloping mitigation with a ball energy sink k_4k_4 k_4 c_4 Square prism The rotative NES k_4 c_4 Uniform transverse air ﬂowc_4 c_4 Figure 1: Schematic drawing of the square prism model with the rotative NES. et al. (2017) performed experiments only to validate the VIV model of the cylinder. Despite a number of theoretical studies concerning various NES designs, few experimental demonstrations are available and even fewer industrial applicationsarereported. ThisispossiblyduetothepracticaldiﬃcultiesofimplementingcomplexNESdesignswith cams, springs and other moving structures. Theautomaticballbalancer(ABB)(Makrametal.,2017)isadiﬀerenttypeofpassivedevicesusedforthereduction ofrotorvibrationgeneratedfromsystemimbalance. AnABBconsistsofmetalballsrotatingfreelyinacirculartrack duetodynamicinteractionwithrotorvibration(Majewskietal.,2015). Theballsarerequiredtoreachacertainposition tocounteractthesystemimbalancethenstoprelativetotherotor. Thesimplicityofsuchbalancershasextendedtheir use to some applications such as optical disc drives (Lu and Hung, 2008) and washing machines (Chen et al., 2015). However,theconceptofABBisdiﬀerentfromarotativeNESthatdependsonenergydissipationtodampthevibrating structure. Whereas ABBs are fabricated with minimal friction to allow the balls to counter the rotary imbalance, a rotativeNESrequiresdissipativeforcesfordamping. Nevertheless,thesimplicityandrobustnessoftheABBishighly inspiring for the design of a rotative NES. This paper experimentally demonstrates the mitigation of the galloping of a square prism due to the dynamic interaction with a purely NES. We use a ball free to roll in a circular track as a simple NES without direct attachment to the primary system. The paper is structured in four sections. Following this introduction, section 2 presents the experimental arrangement and the model description. Section 3 presents the results in three parts: the inﬂuence of the proposed NES on reducing the galloping amplitude, the diﬀerent dynamical regimes, and the eﬀect of the main NES parameters on its behaviour and the prism galloping response. Finally, section 4 brings the conclusion. In the supplementary information, we provide a video succinctly presenting the experimental setup and highlighting the article’s main conclusion. 2. Methodology We performed the experiments in the closed-loop wind tunnel (Model 407-B, ELD, Lake City, MN, USA) of the mechanical engineering department of Polytechnique Montréal. The wind tunnel test section is 6060cm2and the maximum air speed produced is 90m/s. 2.1. Model description Theschematicdrawingofourmodel(Fig. 2)showsasquareprismofsidelength Dmountedontwoidenticalsup- portsofequivalentstiﬀness k,andadampingcoeﬃcient c. Theprismcanonlyvibratetransversely,withdisplacement Michael M. Selwanis et al.: Preprint submitted to Elsevier Page 3 of 14 Wind tunnel demonstration of galloping mitigation with a ball energy sink k ck kc c A square prism Air Flow The proposed NES 0 5 10 15 20 25 Ur0.40.81.21.6A ‘ k cMaximum allowed amplitude With NES Without NES (a) (b) y  k cU D c r  Figure 2: Schematic drawing of the square prism with the rotative NES. y,toafreestreamofvelocity U,resultinginautomaticrotationoftheNESballinacirculartrackofmeanradius r. The ballangulardisplacement ispositivecounter-clockwise. Aballdampingcoeﬃcient caﬀectstheballrotationdueto frictionandairresistance. Theballmovesonahorizontalplane. Hence,itsmotionisnotaﬀectedbythegravitational acceleration. Wedesignedalightweightprismspanningalmosttheentireheightofthewindtunneltestsectionwithouttoomuch blockage eﬀect. Fig. 3(a) presents the square prism model of 5cm side length and 58cm height made of balsa wood and covered with a vinyl smooth. The prism blocks 8.1% of the test section area. Two end plates .2/made of light Formica with 33cm length,13cm width, and 0:1cm thickness installed at the two ends of the square prism prevent airfromescapingthewindtunneltestsection. Anotherpairofsmallerplates(3)of 15cmlengthand 14cmwidthare installed8cm away from each end. These inner plates help approach two-dimensional ﬂow conditions; see Bearman et al. (1987). The square prism is mounted onto two identical elastic supports allowing cross-wise oscillations. Each support consists of two leaf springs (4) as shown in Fig. 3(b). The length of the leaf springs is long compared to the maximumallowedvibrationamplitude. Therefore,thesquareprismisassumedtobehaveasasingledegreeoffreedom (DOF)systemvibratingtransverselytotheﬂow. Freevibrationtestsallowedevaluatingtheequivalenttotaloscillating massM=1:39kg,thenaturalfrequency fn=!_2=2:56,0:01Hzandstructuraldampingratio y=_2=0:01. Inourexperiments,theprismtransversevibrationisrestrictedbytheslotlengthof15cminthetopandbottomboards of the wind tunnel test section, which allows a maximum amplitude Aof7:5cm (equal to 1.5 times the square prism sidelength). Weonlytestedonemassratiofortheprismandcannotinferaboutothermassratiosthatcanbeaquestion of future work, notably modelling work. Table 1 Physical parameters of the experiment. Cross-section side length, D 5cm Prism length, L 58cm Equivalent stiﬀness, k 360N/m Total oscillating mass, M 1.39kg Natural frequency, fn 2.56Hz Structural damping ratio, y 0.01 Critical ﬂow speed, Uc 6.5m/s The lock-in ﬂow speed, Ulock*in=fvsD_St 0.96m/s Onset velocity ratio, =Uc_Ulock*in 6.8 Reduced ﬂow velocity, Ur=U_!D 2.6-28.5 ThispaperprovidesparametricstudyontheeﬀectofmainNESparametersinthenon-dimensionalformforeasier generalization. Consequently, we deﬁne the following dimensionless parameters: the non-dimensional vibration dis- Michael M. Selwanis et al.: Preprint submitted to Elsevier Page 4 of 14 Wind tunnel demonstration of galloping mitigation with a ball energy sink 12 3 415 cm5 6 (a) (b) Figure 3: Experimental set-up showing (a) the model inside the wind tunnel test section and (b) the test section top view. The main components are numbered: (1) the manufactured square prism, (2) outer plates, (3) inner plates, (4) the support that mainly consists of two leaf springs, (5) the NES main body attached to the upper end of the square prism, (6) a slot of 15cm length. placementYandamplitude A;thereducedvelocity Ur;theNESmassratio  mandradiusratio  r;andtherelativeradial clearance that relates the radial clearance between the NES track walls and the ball to the ball radius rb: Y=y D;A=A D; Ur=U !D;  m=mb .M+mb/;  r=r D;  = rb: (1) 2.2. NES design and fabrication WeproposeasimpleNESdesign(Fig. 4)consistingofthemainbody(1),varioussizebushings(2),steelballs(3), andalubricatingﬂuid(4). WebuilttheNEStobeaboutthesizeoftheprismdimensionandmadeitaslightaspossible. A 3D printer (Ultimaker3, Ultimaker) printed the NES components with white Poly-Lactic Acid (PLA) plastic. This modulardesignaimstoeasilyvarythemainNESparametersbyswappingsomeparts. Bushingsofvarioussizesallow varying the racetrack inner and outer radii. Lubrication of the NES track decreases the friction between the rotating ball and the NES body, thus changes the ball damping. 2.3. Measuring system A high-speed Camera (Motion BLITZ Cube 4, MIKROTRON) captured the motion of both the prism and the NES ball with a resolution of 0:085mm to allow for post-treatment image analysis. The memory of the high-speed cameraandtheframedimensionslimittherecordingtimeto40seconds. AMATLABcodewaswrittentoprocessthe recordedimageseriesandplottheprismvibratingdisplacement yandtheballangulardisplacement withtimet. To ensureasteady-state,threeminuteselapsedeachtimebetweensettingthenewwindtunnelﬂowspeedandstartingthe camerarecording. Werepeatedthemeasurementforincrementingﬂowspeedwithincreasingvaluestoplottheprism maximum amplitude A(max abs y(t)) versusﬂow speedUdemonstrating the system response. 3. Results We present the results of this study in three parts: the NES eﬀect on mitigating the galloping of the square prism; the diﬀerent dynamical regimes experienced by the NES; and a parametric study on the NES parameters. Michael M. Selwanis et al.: Preprint submitted to Elsevier Page 5 of 14 Wind tunnel demonstration of galloping mitigation with a ball energy sink 312 4 (a)(c) (d)(b) Figure 4: (a) Exploded view for NES parts: 1- NES main body, 2- various size bushings, 3- steel balls, and 4- a lubricating ﬂuid. (b), (c) and (d) NESs with varing the track dimensions. 3.1. NES Eﬀect on the Prism Response We recorded the dynamics of the prism without NES for incrementing ﬂow speed. To clarify the nature of the vibrations, we compare the critical velocity measured for galloping versus the expected lock-in velocity for VIV. We deﬁne a critical ﬂow speed Ucat which the prism starts to gallop exceeding 4mm amplitude. This speed is observed experimentally as 6:5m/s. Considering a Strouhal number Stof0:133for a square prism (Bearman et al., 1987), the lock-in ﬂow speed of our model Ulock*in=fvsD_St=0:96m/s. Hence, the onset velocity ratio, =Uc_Ulock*in=6:8 (table1),andthesquareprismresponsewithouttheNESshowsapuregallopingwithminimalinteractionwithvortex shedding. We repeated the measurement with a NES of mass ratio  m= 0:08, and a radius ratio  r= 0:6. In this subsection, the measured data is presented in dimensional form without any post-treatment. Fig. 5comparesthemaximumvibrationamplitudesoftheprismwithandwithouttheNESatdiﬀerentﬂowspeeds. Beyond the critical speed Uc, the prism galloping amplitude dramatically increases with the ﬂow speed to exceed the limitofourexperiment 75mmataﬂowspeedof 12:7m/s. TheprismresponsewiththeNES,presentedinFig. 5bythe dashedline,showsasigniﬁcantdecreaseinvibrationamplitude. TheNESmaintainstheprismvibrationdisplacements below5mmuptoaﬂowspeedof 11:2m/s. Withincreasingﬂowspeed,alittlejumpinthevibrationamplitudeoccurs ataﬂowspeedof 12:7m/s. Then,theamplitudeoftheprismwiththeNESplateausuntilaﬂowspeedof 20:2m/s. In this ﬂow speed range, the vibration amplitude does not exceed 30mm. Above this ﬂow speed, the NES is ineﬀective and unable to keep the prism vibration below the maximum allowed amplitude. The NES increases the ﬂow speed at which the prim galloping amplitude reaches the limit of our experiment from 12:7to21:7m/s. Figs. 6(a-c) present the amplitude spectra obtained from the Fast Fourier Transform (FFT) of the vibrating prism displacementinsemi-logscaleatdiﬀerentﬂowspeeds9.7,11.2and 12:7m/s. Figs. 5(a)and(b)comparethefrequency response of the prism with and without the NES. The NES has no signiﬁcant eﬀect on the natural frequency of the prismfn=2:56Hz even at higher ﬂow speed U=12:7m/s where the ball rotates achieving complete revolutions. We can observe that the NES engages with the system dynamics resulting in the transfer of energy from the vi- bratingprismtotheNESintheformofballrotationkineticenergy. Hence,theNESdelaysgallopingoccurrenceand signiﬁcantly mitigates the prism amplitudes for ﬂow speeds between 9:7m/s and20:2m/s. This range of ﬂow speeds canbereferredtoastheNESeﬀectiverange. Athigherﬂowspeeds,thegallopingoftheprismincreasesandtheprism energy is too high to be absorbed by the NES. One of the main advantages of the NES is that it does not change the characteristics of the primary system contrary to other vibration absorbers of linear stiﬀness. Michael M. Selwanis et al.: Preprint submitted to Elsevier Page 6 of 14 Wind tunnel demonstration of galloping mitigation with a ball energy sink 0 5 10 15 20 25 Free stream velocity, U [m/s] Maximum With NESWithout NES 020406080100Transverse amplitude A [mm] Figure 5: The prism responses with and without the NES of mass ratio  m=0.08, and a radius ratio  r=0.6, showing the oscillatory regime ¸, the intermittent regime Ê, and the rotational regime ý. Without NES With NES (a) (b) (c) 10*71 1 1 0 10 0 10 0 10 101 101 f[Hz]10*710*7 Figure 6: The amplitude spectrum of the vibrating prism with NES (red curve) at diﬀerent ﬂow speeds U=: (a)9:7m/s; (b)11:2m/s; (c)12:7m/s. The amplitude spectrum of the vibrating prism without NES (grey curve) is shown only in (a) and (b). 3.2. Diﬀerent NES Dynamics We demonstrate the diﬀerent NES dynamics from the time history of the NES ball angular displacement and its eﬀect on the prism response at diﬀerent ﬂow speeds. The NES experiences three diﬀerent response modes; oscil- latory, intermittent, and rotational. Fig. 7 shows the time histories of the prism displacements and the ball angular displacements at nine ﬂow speeds Ubetween 9 and 20.2m/s. For the three lower speeds, Figs. 7 (a-c) present both the dynamics with and without NES. For Figs. 7 (d-i), Ug12:7m/s, the prism without NES reaches the maximum allowedamplitudeofthesetup. ThebehaviouroftheNESanditsimpactonthedynamicsoftheprismcanbebroken down into three regimes, which we named according to the ball behaviour. Theoscillatoryregime is shown in Figs. 7 (a-c), where the NES ball angular displacement does not exceed 75o. However,itreducestheprismgallopingamplitude. Fig. 7(c)showsasigniﬁcantreductioninthemaximumamplitude by the NES from 70mm to5mm at a ﬂow speed U=11:2m/s. Theintermittent regime , shown in Fig. 7 (d), appears as a transition between two diﬀerent regimes in a small range of ﬂow speeds. The ball rotates with relatively low angular speed keeping the prism vibration amplitude below 28mm. This regime is characterized by a nearly steady vibration for the prism and a ball rotation of a small number of successive complete revolutions not exceeding ﬁve revolutions. Therotational regime appears in a higher range of ﬂow speeds from 14.2 to 20.2m/s, as shown in Figs. 7 (e-i). The prism shows a strongly modulated response of periodic cycles of attenuation and growing vibration amplitude. During each cycle, the prism vibration amplitude grows to reach a maximum value of 30mm, then decreases sharply due to ball rotation. The vibrating prism transfers energy to the NES in the form of kinetic energy resulting in high Michael M. Selwanis et al.: Preprint submitted to Elsevier Page 7 of 14 Wind tunnel demonstration of galloping mitigation with a ball energy sink 0 40 -2020 0 5 10 15 20 25 Free stream velocity, U [m/s] 020406080100Transverse amplitude A [mm] Maximum With NESWithout NES -8080 0 40 0 40 -4040 0 40 -4040 0 40 -4040 0 40 -4040 0 40 -4040 0 40 -4040 (b) (c) (d) (e) (f) (g) (h) (i) -2020 -8080 0 40 0 40 (a) (b) (c) 0 40 -4040 (e) 0 40-4040 (f) -4040 -4040 -4040 0 40 (h) 0 40 (g) 0 40 (i) 0 40 -4040 (d) 0 40 -2020 0 5 10 15 20 25 Free stream velocity, U [m/s] 020406080100Transverse amplitude A [mm] Maximum With NESWithout NES -8080 0 40 0 40 -4040 0 40 -4040 0 40 -4040 (b)(c) 0 40 -4040 (d) 0 40 -4040 (e) (f) (g) 0 40 -4040 (h) (i) (a)(a) -88 Without NES With NES 150350 0 40 250350y[mm] [o] 250350 02000y[mm] [o] -30001000 -40002000 y[mm] [o] -70001000 -70001000 -140001000 0 5 10 15 20 25 020406080100Transverse amplitude A [mm] Maximum With NESWithout NES (a)Free stream velocity, U [m/s] t t t Figure 7: Timehistories y.t/oftheprismdisplacementequippedwithaNES(redcurve)andNESballangulardisplacement .t/in degrees (blue curve) measured at diﬀerent ﬂow speeds U=: (a) 9.0m/s; (b) 9.7m/s; (c) 11.2m/s; (d) 12.7m/s; (e) 14.2m/s; (f) 15.7m/s; (g) 17.2m/s; (h) 18.7m/s; and (i) 20.2m/s. Dynamics of the prism without NES (grey curve) is shown only in (a)-(c). angularspeedsoftherotatingball. TheballrotationandtheconsequentenergydissipationthroughtheTETmechanism drasticallymitigatetheprismgallopingamplitudetolessthan0.1mm. FromFigs. 7(e-i),wecanalsoobservethatthe frequencyoftherepeatedperiodiccyclesofthereducingandgrowingamplitudesincreasesathigherﬂowspeed. The stronglymodulatedresponseofthevibratingprismobservedexperimentallyintherotationalregimeissimilartothat previouslypredictedbyTumkuretal.(2017),anddemonstratestheenergytransferbetweentheprismandtherotative NES during its galloping. At large reduced velocities, beyond the rotational regime, the NES is ineﬀective and the galloping amplitude is abovethelimitsofourexperimentalsetup. Wecansaythattheamountofenergyextractedbythevibratingprismfrom theairﬂowexceedstheenergydissipationrateoftheNES.Anotherhypothesisisthattheinertialcouplingbetweenthe NESandtheprismisnolongerbeneﬁcialatlargeamplitudes. Testingthesehypothesesshouldbepartoffuturework. Michael M. Selwanis et al.: Preprint submitted to Elsevier Page 8 of 14 Wind tunnel demonstration of galloping mitigation with a ball energy sink  m 0.040.08 0.0200.40.81.21.6 0 max .A/ 5 10 15 20 25 Ur (a) 30 5 10 15 20 25 Ur (b)30Oscillatory regimeIntermittentregimeRotational Figure 8: (a) Prism responses without and with a NES of mass ratio  m=0:02(grey marks),  m=0:04(black marks), and m=0:08(white marks) at a constant  r=0:6, (b) NES regimes mapping presenting oscillatory ¸, Intermittent Ê, and Rotational âregimes, and the points that reach the maximum allowed amplitude . 3.3. Inﬂuence of main NES parameters We explore the inﬂuence of each of the main NES parameters individually. The modular NES design presented in section 2.2 allows easy modiﬁcation of the main parameters. Depending on the ball mass, the mass ratio  mcan be varied between 0.02 and 0.08. Bushings of diﬀerent sizes allow varying the NES radius ratio  r(from 0.4 to 0.7) and the NES track relative clearance  (from 0.066 to 0.33). We reduce the ball friction with the NES track by adding a lubricating ﬂuid to investigate the eﬀect of the friction. WecomparetheprismresponsewithvariousNESconﬁgurationsanddeﬁneNESregimesbasedonthediﬀerence between the non-dimensional maximum and minimum vibration amplitudes. This diﬀerence is variable across the diﬀerent regimes :a large value in the rotational regime and a small one in the oscillatory regime. We developed a MATLAB code to automatically categorizes the NES regimes depending on this diﬀerence and plot a NES regime mapping for each conﬁguration of parameters based on the following criterion : ifmax.A/*min.A/>0:2Ùrotational regime, else ifmax.A/*min.A/>0:1Ùintermittent regime, else Ùoscillatory regime. 3.3.1. Mass ratio  m Fig. 8(a)presentsthenon-dimensionalmaximumamplitude Aversus thereducedﬂowvelocities Urfortheprism with NES conﬁgurations with diﬀerent mass ratios  mof 0.02, 0.04, and 0.08, considering a constant radius ratio  r= 0.6 and a relative radial clearance  =0.066. The NES of the smallest mass ratio  m= 0:02reduces the maximum amplitudeinasmallrangeofﬂowspeeds Urf19:2. Formassratios  m=0:04and0:08,theprismmaximumamplitude increasessteadilywithﬂowspeedsuntilreducedﬂowvelocitiesof15.6and13.7,respectively. Then,itjumpsathigher Michael M. Selwanis et al.: Preprint submitted to Elsevier Page 9 of 14 Wind tunnel demonstration of galloping mitigation with a ball energy sink  r0.60.7 0.400.40.81.21.6 max .A/ 5 10 15 20 25 Ur (a) 30 5 10 15 20 25 Ur (b)30 Oscillatory regimeIntermittentregimeRotational Figure 9: (a) Prism responses without and with a NES of radius ratio  r=0:4(white marks),  r=0:6(black marks), and r=0:7(grey marks) at a constant  m=0:04, (b) NES regimes mapping presenting oscillatory ¸, Intermittent Ê, and Rotational âregimes, and the points that reach the maximum allowed amplitude . ﬂowspeedcoincidingwiththeNEStransitionfromtheoscillatorytotheintermittentregimeandcontinueswithslight changes until another higher jump exceeding the limit of the experiment at reduced ﬂow velocities Ur=25 and 27, respectively. This means that increasing the NES mass ratio expands the NES eﬀective range. However, lower mass ratio NES conﬁgurations result in smaller vibration amplitudes in the low-speed range. Fig. 8(b)showsaNESregimemappingforthethreediﬀerentmassratios. Theoscillatoryregimeendsatareduced ﬂow velocity between 14.7 and 16.5 for both mass ratios 0.04 and 0.08. The intermittent regime starts and remains onlyforasmallrangeofvelocitiesuntil Ur=16:5. Whileforthesmallestmassratio,  m=0:02,theoscillatoryregime rangeexpandstoeliminatetheoccurrenceoftheintermittentregime. Forthethreediﬀerentmassratios,therotational regime starts at the same reduced velocity of 16.5 until reaching the maximum allowed amplitude. 3.3.2. Radius ratio  r The behaviour of the NES is greatly aﬀected by the NES radius ratio. A ball of 56g mass and 24mm diameter is usedtoobtainthreediﬀerentradiusratios  r=0:4,0.6and0.7,consideringaconstantmassratio  m=0.04andrelative radial clearance  =0.066. Fig. 9(a) compares the prism responses with the three diﬀerent NES conﬁgurations. The prism with the smaller radius ratio NES oscillates with lower amplitude. The NES eﬀective range at a radius ratio  r= 0:7is smaller than that at lower radius ratios of 0.4 and 0.6. Thus, increasing the NES radius ratio results in increasing the prism vibration amplitudes and decreasing the NES eﬀective range. The NES regime mapping in Fig. 9(b) shows the eﬀect of NES radius ratio variation on the ball behaviour. The oscillating regime range is the same for both radius ratios 0.4 and 0.6 and expands to eliminate the occurrence of the intermittent regime at the radius ratio of 0.7. The intermittent regime is observed from a reduced velocity Ur=14:7 andendsatreducedvelocitiesof20.3and16.5forNESconﬁgurationswithradiusratios0.4and0.6,respectively. For Michael M. Selwanis et al.: Preprint submitted to Elsevier Page 10 of 14 Wind tunnel demonstration of galloping mitigation with a ball energy sink Dry NES 0 00.40.81.21.6 Lubricated NES max .A/ 5 10 15 20 25 Ur (a) 30 5 10 15 20 25 Ur (a) 30 5 10 15 20 25 Ur (b)30Oscillatory regime IntermittentregimeRotational Figure 10: (a) Prism responses without and with a dry (white marks) and lubricated (black marks) NESs with the same mass and radius ratios  m= 0:08, r= 0:6, (b) NES regimes mapping presenting oscillatory ¸, Intermittent Ê, and Rotational âregimes, and the points that reach the maximum allowed amplitude . the highest value of radius ratio  r=0:7, the rotational regime starts directly after the oscillatory regime at a reduced velocityof16.5. Thestartingreducedvelocitiesoftherotationalregimeare20.3,16.5,and16.5atthediﬀerentradius ratiosof0.4,0.6and0.7,respectively. Hence,increasingtheNESradiusratiohasasigniﬁcanteﬀectinnarrowingthe intermittent regime range. 3.3.3. Ball friction The ball damping ratio has an important eﬀect on the NES behaviour. Ball damping comes predominantly from the friction between the ball and the NES track. It is diﬃcult to get an exact value for the ball damping ratio as it depends on uncertain parameters such as air resistance, and the ball behaviour (rolling or slipping). We added lubricating oil to reduce the ball friction with the NES track walls. We tested a lubricated and a dry NESs with the same parameters  m=0:08, r=0:6and =0:066to investigate the eﬀect of ball damping variation. The prism responses with the two NES conﬁgurations are presented in Fig. 10(a). The lubricated NES is more eﬀectivethanthedryoneinreducingthegallopingamplitudesoftheprismatthereducedﬂowvelocities 13:6<Ur< 17:4. Fig. 10(b)showstheNESregimemappingforboththelubricatedandthedryNES.Theoscillatoryregimerange expandsinthecaseofthelubricatedNEStoeliminatetheappearanceoftheintermittentregime. Whiletherotational regime range is delayed by the lubricating ﬂuid to start at a reduced velocity Ur= 19:3instead of17:4. A possible explanation for this ﬁnding is that the ball can rotate with higher angular speeds and absorb more energy from the system in the presence of lubrication due to decreased friction. 3.3.4. NES track relative clearance   Increasing the radial clearance  aﬀects the ball rotation and increases the magnitude of the impacts between the ball and the NES track walls leading to diﬀerent dynamics. Changing the inner bushing size allows achieving three Michael M. Selwanis et al.: Preprint submitted to Elsevier Page 11 of 14 Wind tunnel demonstration of galloping mitigation with a ball energy sink 0.066 0 00.40.81.21.6 0.33  0.2 max .A/ 5 10 15 20 25 Ur (b) 305 10 15 20 25 Ur (a) 30 Oscillatory regime IntermittentregimeRotational Figure 11: (a) Prism responses without and with NESs of varying track relative clearance;  =0:066(white marks),  = 0:2(black marks), and  = 0:33(grey marks) at a constant mass and radius ratios  m= 0:08, r= 0:66,0:01, (b) NES regimes mapping presenting oscillatory ¸, Intermittent Ê, and Rotational âregimes, and the points that reach the maximum allowed amplitude . relative NES track clearance values of 0.066, 0.2, and 0.33 for the same NES of mass ratio  m=0.08 and radius ratio  r=0:61,0:01. The NES responses, presented in Fig. 11(a), are highly aﬀected by the radial clearance. Increasing the radial clearance reduces the prism galloping amplitude, however, it does not change the NES eﬀective range. Fig. 11(b) presents the NES regime mapping for the three diﬀerent radial clearances. Increasing the radial clearance widens theoscillatoryregimerangeandshiftstheintermittentregimewithnochangeinitsrange. Weobservetheoscillatory regimeuptoreducedﬂowvelocitiesof14.7,18.3,and20.2atdiﬀerentradialclearancesof1,3,and5mm,respectively. TheﬁndingsathigherradialclearancemaybeexplainedbytheeﬀectoftheballimpactwiththeNEStrackwallsthat appear as an additional way for nonlinear energy absorption. 4. Conclusion ThetypicalformofarotativeNESpresentedintheliteratureconsistsofatipmasscoupledtoaprimarystructureby arigidbarofﬁxedlength. Inthisresearch,wedesignedanewrotativeNESusingafreemetalballmovinginacircular track without direct coupling to the primary system proposing a simple, robust and eﬀective way of nonlinear energy absorption. Atleasttotheauthors’knowledge,experimentalinvestigationfocusingonthegallopingsuppressionusing NES is not found in the literature and is the major novelty of this paper. TherotativeNESproposedinthisstudysuccessfullymitigatesthegallopingofasquareprismwithnoeﬀectonits naturalfrequency. WindtunnelexperimentsexposedthemechanismofactionoftheproposedNESandhighlightedits three diﬀerent response modes :oscillatory regime, intermittent regime, and rotational regime. At low ﬂow speeds in Michael M. Selwanis et al.: Preprint submitted to Elsevier Page 12 of 14 Wind tunnel demonstration of galloping mitigation with a ball energy sink theoscillatoryregime,theNESballoscillateswithasmallamplitudenotexceeding70degrees,however,itincreases thecriticalgallopingvelocity. Athigherﬂowspeeds,theintermittentregimeappearswithinasmallﬂowspeedrange. Theballoscillateswithrelativelylowangularspeedstokeeptheprismamplitudelessthan 30mmresultinginanearly steady vibration of the prism. At higher ﬂow speeds still, the rotational regime shows the maximum reduction for the prism vibration, where the NES ball rotates with high angular speeds and absorbs a high amount of energy. The ball rotation directly reduces the prism vibrations resulting in periodic cycles of reduction and growing in the prism vibration displacement. ThedesignoftheNESallowsforeasychangesofitsmainparametersbyswappingsomecomponents. Capitalising onthisadvantage,weexperimentallyquantiﬁedtheinﬂuenceofthemainNESparametersonboththeprismgalloping response and the NES regime mapping over ﬂow velocities. Increasing the mass ratio increases the NES eﬀective range, and leads to the appearance of the intermittent regime coinciding with a small jump in the prism amplitude response. On the contrary, increasing the radius ratio decreases the NES eﬀective range, and reduces the intermittent regimerangerisingtheprismvibrationamplitudes. DecreasingtheballfrictionwiththeNEStrackincreasestheNES eﬀective range, and reduces the intermittent regime range. Hence, it eliminates the small jump in prism amplitude coinciding with the starting of the intermittent regime. We highlight the clearance between the NES track walls and the rotating ball as an eﬀective parameter. Increasing the radial clearance signiﬁcantly reduces the prism vibration amplitudes. For the range of parameter values considered here, the most eﬃcient NES possess the highest mass ratio and radial clearance, and the lowest radius ratio. The simple structure of the presented NES may extend its usage to many applications. It can damp wind-induced galloping on diﬀerent types of structures such as power lines, high mounted signboards, long slender structures and skyscrapers. Ourexperimentsarelimitedtoamaximumnon-dimensionalamplitudeof1.5. Consequently,anaccurate numerical model is important in future work to predict the NES behaviour and prism dynamics at high vibration amplitudes. These mathematical models are under development. Acknowledgements We acknowledge the Military Technical College (MTC) in Egypt and the Natural Sciences and Engineering Re- search Council of Canada (NSERC) for sponsoring the current project. The second author acknowledges the Fonds de Recherche du Québec – Nature et technologies (FRQNT) for sponsoring his short-term period (from December/ 2017 to February/ 2018) as a visiting researcher at Polytechnique Montreal. We want to thank Alexandre Medeiros, and Constant Roussel for their work in developing the experimental setup, as well as Sima Rishmawi for her help in image processing. We are also grateful for the insightful comments oﬀered by Raed Bouslama.