Design of a Wind Tunnel Apparatus to assist Flow and Aeroelastic Control via Zero Net Mass Flow Actuators

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1 Design of a Wind Tunnel Apparatus to assist Flow and Aeroelasti Control via Zero Net Mass Flow Atuators Keegan S. O Donnell *, Piergiovanni Marzoa, Attilio Milanese Carles MNall, Ratneswar Ja, Erik M. Bollt Clarkson University, Potsdam, NY, Abstrat A plunging-piting aeroelasti apparatus as been developed to experimentally test new devies for flow and aeroelasti ontrol. Te purpose of te experiment is twofold: i) te first pase investigates te aeroelasti beavior of a two-dimensional wing setion in postflutter region, struturally and aerodynamially araterizing te aeroelasti model; ii) te subsequent experiment will be instrumental to test ative flow ontrol devies in bot te pre- and post-flutter regimes. Te design of te testing apparatus utilizes a linear and nonlinear am spring system tat allows testing at seleted aeroelasti and flowfield onditions. Te wing setion is mounted to te aeroelasti test apparatus and tests ave been onduted in te low speed Clarkson University Wind Tunnel Faility. Plunging and piting aelerations of te wing during aeroelasti response ave been reorded to study and ompare te experimental results wit te proposed matematial models. Ative flow ontrol devies are ben tested and will be installed in a omposite NACA 18 airfoil at speified loations along te wing span. Zero net mass flow atuators (ZNMF) are onsidered in tis resear: ZNMF ontrol devies, su as synteti jets atuators (SJA) and frequeny driven voie oils, are under investigation to demonstrate teir ability to atively ange te flowfield for improved aeroelasti wing performanes. Numerial simulations ave already demonstrated improved performane regarding flow and aeroelasti arateristis due to ative flow ontrol. Experimental investigation, numerial studies, and orresponding analytial models are provided and pertinent onlusions are disussed. Nomenlature a = Nondimensional elasti axis loation ab = Loation of te elasti axis from te middle ord α = Piting displaement b = Mid-ord = Plunging damping oeffiient α L L L d I α k α = Piting damping oeffiient = Aerodynami lifting fore = Aerodynami lifting fore due to SJA = Aerodynami disturbane = Plunging displaement = Total piting inertia = Torsional spring stiffness * Graduate Resear Assistant, Meanial and Aeronautial Engineering Department, Member AIAA Assistant Professor, Meanial and Aeronautial Engineering Department, Member AIAA. Graduate Resear Assistant, Meanial and Aeronautial Engineering Department, Member AIAA Undergraduate Student, Meanial and Aeronautial Engineering Department Assoiate Professor, Meanial and Aeronautial Engineering Department, Assoiate Fellow AIAA Professor, Matematis and Computer Siene Department 1

2 k m M M M m m s t w d T U = Plunging spring stiffness = Total wing mass = Aerodynami moment about te elasti axis = Aerodynami moment due to SJA = Aerodynami disturbane = Pit am mass = Total plunging mass = Wing span = Time = Free stream veloity I. Introdution Aeroelasti indued responses our due to te interation of aerodynami, inertial and elasti fores. Certain aeroelasti instabilities, su as flutter, an jeopardize lifting surfaes performane and survivability [1]. In te safe fligt envelope te natural modes (e.g. bending and torsion of lifting surfaes) do not interat. Te linear flutter boundary veloity orresponds to a oalesene of two modes and marks te onset of aeroelasti instabilities, leading in extreme ases to atastropi failures. Due to inerent strutural and aerodynami nonlinearities, te flutter beavior often appears in form of stable onstant amplitude osillations, known in literature as limit yle osillations (LCOs). Depending on te nonlinearities of te system and te fligt operating onditions LCOs an sow a wide range of amplitudes and frequenies. Te arateristis of tis penomenon an be redued to a simplified two degrees of freedom pit- and plunging model. A great deal of resear ativity devoted to te aeroelasti ative ontrol and flutter suppression of fligt veiles as been aomplised. Te two main fundamental objetives of flow ontrol devies are: i) ontrol of aeroelasti vibrations and ii) suppression of dynami aeroelasti instabilities, su as flutter and non-linear LCOs. Te state-ofte-art advanes in tese areas are presented by Dowell [] in is latest edited monograp wi disusses te urrent teoretial, omputational and experimental resear onduted in te field of nonlinear aeroelastiity. Witin te aeroelasti experimentations onduted in te resear ommunity, te group led by Strgana at te University of Texas A&M as made major ontributions and as extensively investigated nonlinear plunging and piting aeroelasti models in low speed wind tunnel testing. A portion of teir resear as enompassed two wing setions wit leading and trailing edge ontrol surfaes used for aeroelasti suppression []. Blok et al. [3] used a full-state feedbak ontroller tat demonstrated te ability to stabilize te nonlinear aeroelasti testing apparatus system at twie te open loop flutter veloity. Also, passive ontrol teniques were explored by Hill et al. [4] tat demonstrated a nonlinear energy sink devie to be effetive in inreasing te overall stability tresold of te aeroelasti system. In reent years, several ative linear and nonlinear ontrol apabilities ave been implemented. Digital adaptive ontrol of a linear aeroservoelasti model, are only a few of te latest developed ative ontrol metods [5-7]. One lass of ative flow ontrol devies tat as garnered numerous teoretial and experimental investigations are zero net mass flow (ZNMF) atuators. ZNMF atuators are different from traditional ontrols su as flaps and spoilers in tat tey use no meanial devies to diretly alter te flowfield. Rao et al. [8] araterized eletrial motor driven synteti jet atuators (SJAs) using partile imaging veloimetry (PIV) in a water tunnel and sowed te ability to delay separation on te airfoil. Furtermore, a piezoeletri atuator driven at 63.5 [Hz] was reported to produe a mere 1.87 [m/s] exit veloity wen installed in a stati wing onfiguration [8]. Many researes ave improved te performane of piezoeletri SJAs, for example Gallas et al. [9], ave sown tat osillating te piezoeletri membrane at its natural frequeny an result in exit veloities between 3 and 5 [m/s]. Te resear performed at Clarkson University inludes wind tunnel experiments for aeroelasti responses and te appliability of ZNMF atuators in ative flow ontrol semes. Te teoretial and numerial models proposed in previous resear needs to be validated troug experimental testing [1]. To ompliment te numerial efforts an aeroelasti test apparatus was designed to aommodate te parameters defined by te aeroelasti arateristis of te presribed wing setion. Te system as been designed for ease of use and adaptability for future installation of

3 ative flow ontrol devies tat will be tested in an aeronautial low speed wind tunnel. Te presribed wing features a omposite sell wit a symmetri NACA 18 profile. Due to te pysial onstraints of te wing it is onsidered to be rigid, wit all te elasti properties onentrated in te springs and am system. Te onstruted test apparatus is based on existing test beds developed at Texas A&M University and NASA Langley Resear Center [4, 15]. Te apparatus features independent pit and plunge movement tat will allow te wing to exibit plunging piting flutter and LCO at a ertain frequeny and dynami pressure. Te rest of te paper is organized as follows. Setion II ontains preliminary alulations and modeling based on basi aeroelasti teory. Setion III gives insigt into te experimental setup. Setion IV details te results of te experimental testing, and Setion V disusses te ontrol objetive and planned experiments. Setion VI summarizes te onlusions of te paper. II. Preliminaries on te Aeroelasti Teory and Analytial Modeling Te aeroelasti system is modeled as a wing setion tat allows for two degrees of freedom. Te wing setion is mounted so tat piting and plunging are permitted as illustrated in Fig. 1. For tis model te aeroelasti governing equations for te -DOF system an be written as follows [3,1,13]: Figure 1: -DOF piting and plunging wing setion. m + mx b α α + + k = L( t) + Ld ( t) + L ( t) (1) I α + mx b + α + k ( α) α = M ( t) + M ( t) + M ( t) () α α α α were te strutural nonlinearities are retained in te equations of motion [15]. In equations (1) and () L( t ) and M ( t) are te aerodynami lift and moment respetively; L d and M d are aerodynami flow disturbanes, su as gust loads, wile L and M are te external loads due to te SJAs. Te aerodynami lift and moment in quasisteady form tat ave been used in te analytial model are represented in equations (3) and (4). d ( ) α ( t) t 1 L( t) = ρ U blα α ( t) + + a b (3) U U M ( t) = b L( t) (4) In tis preliminary analysis only linear quasi-steady aerodynami loads ave been onsidered, owever modifiations to inlude seondary effets and flow separations are also ontemplated. As in te atual test apparatus, te analytial model onsiders te plunging and piting displaements to be restrained by springs wit stiffnesses denoted as K and K ( ) and are attaed at te elasti axis of te wing setion. In tis ase, K ( ) represents te ontinuous nonlinear restoring moment in te pit degree-of-freedom. Te previous models ave suessfully produed analytial numerial solutions to te nonlinear oupled aeroelasti governing equations of motion [1,18]. However, autors ave reported disrepanies between te experimental measurements and te analytial analysis [11]. Tese disrepanies an most likely be aounted for in te Coulomb damping fores tat our witin te pit bearing and plunge slider motion tat is not taken into aount in many of te models. At low veloities, damping is mu greater tan at iger veloities reating nonlinear 3

4 [m] damping. Coulomb damping an be represented in te governing equations as a fore opposing te motion of te system. A diret relationsip exists between te damping and frition terms beause te damping beomes negligible as soon as te frition fore is greater ten te restoring fore. Tus te system an not experiene aeroelasti osillations wen te restoring fore is less ten te frition and damping Plunge Displaement fores. Wen Coulomb damping is aounted. for in te aeroelasti model, te equations for.1 te plunge and pit damping fores are as follows: -.1 F = µ mg 1 (5) -. Fα = µα M f α α 1 (6) Pit Displaement Herein M f is te fritional moment due to te nonlinear am and µ, µα are te fritional oeffiients, wi an be determined for example by means of te deaying peak amplitudes [3]. In a straigtforward manner, te aeroelasti governing equations (1) and () aounting for (5) and (6) an be onverted into te equivalent state-spae form, wi is more suitable for te implementation of a ontrol [1,14]. III. [rad] Figure : Analytial aeroelasti LCO response for quasisteady aerodynamis. Experimental Setup Clarkson University Aeroelasti Test Apparatus In tis setion, we desribe our implementation of te test apparatus wi was used to experimental araterize aeroelasti properties. Two similar test apparatus designed at NASA Langley and University of Texas A&M ave aided researers in developing teir plunging-piting devies and in araterizing te aeroelasti properties of su systems [14-17]. Te ability to demonstrate suppression of aeroelasti instabilities su as LCO and flutter troug ZNMF as neessitated te design and development of su aeroelasti apparatus. Figure 3: Exploded and assembled semati of aeroelasti apparatus and installation in Clarkson University low speed wind tunnel. Figure 3 sematially depits te omplete assembly of te -DOF test apparatus developed at Clarkson University. Su a design allows for independent piting and plunging motions. To aomplis tis kinemati 4

5 deoupling a bearing arriage system was utilized. Te irular bearing, wi allows for te pit motion, is pressed into a arriage tat is diretly attaed to te slider bearing allowing for motion in te plunge diretion. Due to te large antilevered nature of te wing, a onsiderable moment is translated troug te bearing and onto te linear plunging system. A robust solution to elp overome te fores and keep te system from binding used slider drawer bearings rated for ig moment loads. Te nonlinear spring am retention system sown in Fig. 3 is omprised of a nonlinear am mounted to te rotational axis to restrit pit movement and a linear am mounted in line wit te slider art to restrit plunge displaement. Te omposite design of te wing is onsidered perfetly rigid witin te parameters of our testing; terefore te elastiity of te system is inerently ontained ompletely in te spring am system. Te main advantage of te system is tat te springs onneted to te ams as sown in Fig 3 are easily interangeable allowing for parametri stiffness tests to be onduted. Te initial stati and dynami tests will elp to araterize te Coulomb damping oeffiients and. One te damping ontributions ave been araterized, tese an be inluded in te analytial model to better investigate LCOs at low veloities. Te parameters for te experimental apparatus are listed ereafter, a = = 1.41Nm s I α =.3kgm b =.15m l α = 6.81 rad 1 1 α =.16Nm s α = ( ) m.5 a l α + t m w =.49kg m =.1kg x α = ( + ) m = 1.59kg.873 b ab b Te nonlinear pit stiffness is related to te atual springs onstant troug te geometry of te am and te attament points, as sematially represented in Fig. 4. Using a oordinate transformation te tangential ontat point for a given am rotation an be determined; using te orresponding arm lengt te nonlinear restoring moment an be omputed as a funtion of te pit angle, and ene te stiffness an be derived. For te presented apparatus, te nonlinear restoring moment took on te 5 t order polynomial form as follows: 5 i= 1 i 1 kα ( α) = τ iα (7) To aurately measure te aeroelasti response of te piting-plunging apparatus aelerometers were mounted to te leading and trailing edge of te wing setion sown in Fig. 5. Te trailing edge and leading edge aelerometers are indiated by ate and a LE, respetively; b TE is te distane between te trailing edge and te elasti axis, ble is te distane between te leading edge and te elasti axis, θ is te angle aused by te leading edge geometry at te attament of te aelerometer, and, α are te wings plunging and piting aeleration respetively. Figure 4: Nonlinear Cam LE a = b α + (8) TE TE ( LEα ) sin ( θ ) a = b + (9) Equations (8) and (9) are solved for te piting and plunging aelerations, α and, respetively. Te two aelerometers voltage outputs ave been resolved into te piting and Figure 5: Semati of wing mounted aelerometers 5

6 plunging motion about te elasti axis. To ek te auray of te orrelation an aelerometer was fixed to te apparatus arriage to diretly measure te plunging aeleration. All of te voltage signals were onverted to aeleration, veloities, and displaements were olleted using LABVIEW and reorded to a text output file tat was post proessed in MATLAB. IV. Experimental Results Te experimental data were used to obtain aurate damping terms. Coulomb damping is defined by a fore restraining te motion of system, regardless of diretion as sown in equations (5) and (6). In order to obtain te pit and plunge damping terms independently, ea free vibration ase was run wile loking down te oter degree-of-freedom [3]. Wen te system is released into free vibration tere is an inerent restoring fore reated by te springs in bot te plunge and piting degrees-of-freedom, tis restoring fore will keep te system in motion until te Coulomb damping and finally frition fores beome greater ten te overall restoring fore. Reording te veloity time istories data for te free vibration ase in Fig. 5, and assoiating te deaying peak amplitudes, a Coulomb damping model was reated for analytial use. Cases were run for ea spring set used in te experiment, te spring onstants were 576, 64, 1186 [N/m] for sets 1,,3 respetively. It is wort mentioning tat Fig. 5 and 6 ontain also te aerodynami damping fores, sine te wing setion is attaed to te system during te experiment. Te resultant time istory ases sown in Fig. 5 and 6 represented te total damping of te system. Terefore µ and µ α are given by te following: A (1) 4g Veloity [m/s] Free Vibration: Plunge Damping (No Wing) Plunge Spring 1 Plunge Spring Plunge Spring TIme [se] Figure 5: Free vibration response for different plunge spring onstant.6.4. Free and Fore Vibration Plunge Damping (Wit Wing) Free Vibration Wind Veloity 5 m/s Wind Veloity 6 m/s A (11) -. 4g -.4 ere te deaying peak amplitudes are represented by A of te free vibration -.6 ases [3]. Tis model was ten ompared -.8 to fored vibration ase for two tunnel -1 wind veloities of 5 and 6 [m/s] and Time [se] plunge spring stiffness eld onstant at 1186 [N/m]. Fig. 6 represents te Figure 6: Free and fored vibration response for plunge spring experimental fored vibration veloity stiffness k = 1186 [N/m], sub ritial free stream veloity versus time under-damped ase for te system in te plunge diretion. It an be observed tat, as te system approaes te flutter boundary, te Coulomb damping beomes less important. A parametri study of varying plunge spring stiffness k was tested wile olding onstant te nonlinear pit Veloity [m/s] spring stiffness k α ( α ). During testing te free stream veloity U was started below te flutter boundary veloity and gradually stepped up until LCO or divergent flutter was reaed. 6

7 6 Piting Displaement.4 Plunging Displaement Displaement [rad] Displaement [m] Piting Pase Diagram 5 Plunging Pase Diagram Veloity [rad/s] 5-5 Veloity [m/s] Displaement [rad] Displaement [m] Figure 7: Time istory and pase diagram for LCO response at 5 [m/s] Figures 7 sows a typial stable LCO response for a plunge spring stiffness of 64 [N/m] and a free stream veloity of 5 [m/s]. Te study sowed tat average LCO amplitudes varied from.85 to.175 [m] in te plunge diretion and 5 to 15 [deg] of piting rotation depending on te plunge spring stiffness. Also te LCO frequenies oalesed at values from 6 to 7.5 [Hz]..4 Piting Displaement. Plunging Displaement Displaement [rad]. -. Displaement [m] k = 578 [N/m], U = 5. [m/s] k = 64 [N/m], U = 5.8 [m/s] k = 1186 [N/m], U = 7.8 [m/s] Figure 8: LCO responses for seleted plunging spring stiffnesses (k) Figure 8 grapially depits te time istory LCO response for te tree plunge spring stiffness k ases. Te first two ases sow very similar LCO amplitudes and ritial free stream veloities; tis is most likely due to similar spring stiffness values. 7

8 Plunge Aeleration FFT 4 x k = 578 [N/m], U = 5. [m/s] k = 64 [N/m], U = 5.8 [m/s] k = 1186 [N/m], U = 7.8 [m/s] freq [Hz] Figure 9: FFT of LCO response at seleted plunging spring stiffness Wen te k value was inreased to 1186 [N/m] te stable LCO is obtained at 7.8 [m/s]. Te orresponding FFT are grapially sown in Fig. 9. Te results of Fig. 8 sow tat as k is inreased te independent pit and plunge motion frequenies oalese at a larger value. Generally te experiment sowed tat a larger te plunge spring stiffness k resulted in smaller LCO amplitudes and iger frequenies. Anoter means of araterizing te aeroelasti system is by exploring te bifuration plots. Many bifuration plots are represented in te form of LCO amplitude versus anoter system parameter su as wind tunnel veloity. By observing nonlinear bifurations, aeroelasti responses an be determined in te viinity of te flutter boundary. Tis nonlinear analysis an determine te LCO stability. In Fig. 9 a general bifuration plot depits two different LCO responses [1]. It an be learly seen tat wen weakly nonlinearities are present in te aeroelasti system te LCO quikly rea large amplitude wit a onsequent divergent beavior. Conversely, strong nonlinearities reate a more stable LCO response. To explore tis penomenon a seond parametri study was onduted on te aeroelasti test apparatus. Te investigation aided in exploration of te effets te nonlinear spring α and its interation wit te linear k α stiffness ( ) plunge spring k as sown in Fig. 11. Figure 1: Bifuration plot sowing two main LCO arateristis 8

9 LCO Amplitude [deg] LCO Amplitude [deg] 4 Bifuration Plot (Plunge Spring Stiffness = [N/m]) k = Pit Spring Stiffness Bifuration Plot (Plunge Spring Stiffness = 76.8 [N/m]) k = LCO Amplitude [deg] Bifuration Plot (Plunge Spring Stiffness = 966 [N/m]) Wind Tunnel Veloity [m/s] Figure 11: Bifuration plots, arrows represent ritial boundary veloity Te experimental data depited in Fig. 11 give insigt into te relationsip of te nonlinear pit and te linear plunge springs were te arrows represent te ritial flutter boundary speed. Te bifuration plots sow tat for iger spring stiffness, bot k α ( α ) and k, a stable LCO is maintained for a larger range of wind speeds. Also a general trend is witnessed between te plunge and spring stiffness relationsip. Te preliminary results sow tat for larger k te ritial flutter boundary ours at iger veloities for smaller ( ) k α α values. More exaustive test will be onduted for a wider range of spring stiffnesses to aide in te full understanding of tis penomenon. [m] Pit Displaement [rad] Plunging Time History Piting Time History.4 Analytial. Experimental -. Analytial Experimental Figure 1: Analytial and Experimental response for plunge spring k = 64 [N/m] and free stream veloity = 5.8 [m/s] 9

10 On ompletion of te experimental parametri studies, te pysial parameters of te apparatus were applied to te analytial quasi-steady aerodynami model for qualitative omparisons. All te pysial parameters of te system are given in te experimental setup setion. Te analytial model used te general equations of motion (1) and (), wit te aerodynami loads of (3) and (4), rewritten in state-spae form: a diret numerial integration as been performed wit a Runge Kutta seme, as implemented in te MATLAB ODE45 solver. Fig. 1 grapially represents te omparison between experimentally reorded displaement time istory and analytially omputed displaement response for te same spring onstants and free stream veloity. Te analytial model sows a very good orrelation wit te experimental data in amplitude and a sligt differene in frequeny. Tese disrepanies are urrently being investigated, in partiular furter analyzing te possible soures of unertainties in te model, su as te overall ompliane of te struture, mass unbalane, and oter damping meanisms. Te validated analytial model will be used as a tool for ontrol teory appliations and witin te formulation of te proper ontrol laws. Tis resear is on-going and preliminary results and disussions are presented in [1]. V. Appliation of ZNMF for Ative Flow and Aeroelasti Control A. Preliminaries on SJAs Ative flow and aeroelasti ontrol are multidisiplinary resear areas ombining flow pysis, sensing, ontrol and atuation wit te goal of anging te flowfield arateristis to enane and inrease te aerodynami and strutural performanes [18]. Te SJAs are in te lass of ZNMF atuators beause tey require no input mass but produe a non-zero momentum output. Te two basi omponents of and SJA are te avity and te osillating diapragm sematially depited in Fig. 13. Te installation of SJAs will give te wing te apability to atively ange its boundary layer. Te altering of te boundary layer as enabled and proven tat tese devies an elp drag redution, lift enanements, mixing augmentations and flow-indued noise suppression [1]. Promising resear onduted by Duvigneau and Visonneau reported a stall delay from 16 to [deg] and a inrease in te maximum lift of +5% wit respet to te baseline airfoil for optimal parameters [8]. Te work previously onduted on optimization and te ontrol parameters will be taken into onsideration and implemented in te seond pase of testing. To supplement te work being arried out at Clarkson University, te design and optimization of synteti jets to be used in tis resear are being onduted in ollaboration wit Delft University of Tenology, Te Neterlands [1]. A. Synteti Jet Atuation Future Experiments Figure 13: Semati of synteti jet atuator (SJA) A stereolitograpy NACA 18 setion (sown in Fig. 14) was designed to test and validate SJAs. Te wing setion inorporates internal pressure taps and an be mounted to a fore balane to quantify te resulting differene between atuation and no atuation Figure 14: Semati of sterolitograpy model wit installed atuator, internal pressure tapings, and interangeable orifies setion. 1

11 for seleted values of te angle-of attak and te atuation frequeny of te SJA. Te fore balane as a manual rank to aurately ange te angle-of-attak. A basi potentiometer iruit is used to vary te frequeny of atuation. Furtermore, two orifie designs will be tested. Te first design will use a 1 mm exit ole diameter, wile te seond orifie will use a 1 mm slot running aross te diameter of te atuator. Initial open-loop experiments an be used to develop a omplete understanding of SJAs effets on boundary layer separation and on te unsteady aerodynami lift and moment. After aquiring tis experimental knowledge an aurate translation of te pysis of SJAs to te omputational domain an be made. Furtermore, a losed-loop ontrol law an be developed and tested to study te performane of te SJAs in suppressing aeroelasti instabilities and enane lifting surfae performanes. VI. Conluding Remarks A two-degree of freedom aeroelasti test apparatus as been designed, built and instrumented to aide in experimental investigations. Preliminary tests onduted in te Clarkson University low speed wind tunnel faility as sown tat te nonlinear aeroelasti apparatus is apable of aieving flutter and LCOs. A parametri study was arried out to assess te effet of several linear and non-linear stiffnesses on te system. Low speed testing sowed LCO plunging amplitudes from.15 to.4 [m] and piting amplitudes from.1 to.35 [rad] wit frequenies varying from 3 to 7.5 [Hz] depending on stiffness onfigurations. As a general trend, te aeroelasti system wit larger stiffness exibited te smaller amplitudes and iger frequenies LCO. Furtermore, a preliminary relationsip between plunge and pit spring stiffnesses was developed. More testing needs to be onduted to aide in te full understanding of te systems linear and non-linear stiffness and damping interations. Te experimental data was orrelated wit te developed analytial model tat will elp in te reation and implementation of ative flow ontrol semes by mean of ZNMF. Finally, installed atuators will be tested on te aeroelasti apparatus wit te ultimate goal of effiiently improving te overall aeroelasti performane of te system. Aknowledgments Te autors would like to aknowledge partial support for tis resear from te MDA under ontrat # , Clarkson University Sool of Engineering seed grant, te NSF-REU and MNair Programs for supporting Carles MNall summer internsip. 11

12 Referenes 1. Libresu, L., Marzoa, P., Advanes in te Linear/Nonlinear Control of Aeroelasti Strutural Systems, Ata Meania, Vol. 178, No. 3-4, August 4, 5, pp Dowell, E.H., Clark, R., Cox, D., Curtiss, H.C Jr, Edwards, J. W., Hall, K. C., Peters, D. A., Sanlan, R., Simiu, E., Sisto, F., Strgana, T. W., A Modern Course in Aeroelastiity, Fourt Revised, Kluwer Aademi publisers, opyrigt (4). 3. Blok, J. J., Gilliatt, H., Ative Control of an Aeroelasti Struture AIAA, Aerospae Sienes Meeting & Exibit, 35 t, Reno, NV, Jan. 6-9, AIAA Paper Texas A&M University, College Station, Texas, Hill, W., Strgana, T., Nikawde, C., Suppression of Aeroelasti Instability wit a Nonlinear Energy Sink: Experimental Results, 47 t AIAA/ASME/ASCE/AHS/ASC Strutures, Strutural Dynamis, and Materials Conferene, 1-4 May 6, Newport, Rode Island. 5. Mukopadyay, V. (ed.), Benmark Ative Control Tenology, Pt., Journal of Guidane, Control, and Dynamis, Vol. 3, No. 6,, pp Mukopadyay, V. (ed.), Benmark Ative Control Tenology, Pt. 3, Journal of Guidane, Control, and Dynamis, Vol. 4, No. 1, 1, pp Mukopadyay, V., Historial Perspetive on Analysis and Control of Aeroelasti Responses, Journal of Guidane, Control, and Dynamis, Vol. 6, No. 5, 3, pp Rao, P.P., Strgana, T.W., Rediniotis, O. K., Control of Aeroelasti Response Via Synteti Jet Atuators, 41 st AIAA/ASME/ASCE/AHS/ASC Strutures, Strutural Dynamis, and Materials Conferene, AIAA , Atlanta, GA, 3-6 April. 9. Gallas, Q., Holman, R., Tosikazu, N., Carroll, B., Seplak, M., Cattafesta. L., Lumped Element Modeling of Piezoeletri-Driven Synteti Jet Atuators, AIAA Journal, Vol 41, No., February (3). 1. O Donnell, K., Sober, S., Stolk, M., Marzoa, P., De Breuker, R., Abdalla, M., Niolini, E., Gurdal, Z., Ative Aeroelasti Control Aspets of an Airraft Wing by Using Synteti Jet Atuators: Modeling, Simulations, Experiments, Te 14t International Symposium on: Smart Strutures and Materials & Nondestrutive Evaluation and Healt Monitoring, SPIE 653-8, San Diego, CA, 18- Mar Duvignequ, R., Visonneau, M., Optimization of a Synteti Jet Atuator for Aerodynami Stall Control, Elsevier, Laboratorire de Meanique des Fluides CNRS UMR 6598, Eole Centrale de Nantes, B.P. 911, rue de la Noe FR-4431, Nantes edex 3, Frane, 13 January Blok, J.J., Strgana, T.W., Applied Ative Control for a Nonlinear Aeroelasti Struture Journal of Guidane, Control, and Dynamis, Vol. 1, No.6, pp (1998). 13. C. Rubillo, P. Marzoa, E. Bollt, Ative Aeroelasti Control of Lifting Surfaes via Jet Reation Limiter Control, International Journal of Bifuration and Caos, Vol. 16, No. 9, 6, O Neil, T., Experimental and Analytial Investigations of an Aeroelasti Struture wit Continuous Nonlinear Stiffness, Texas A&M University Masters of Siene Tesis, May O Neil, T., Stragana, T.W., Aeroelasti Response of Wing Supported by Nonlinear Springs, Journal of Airraft, Vol. 35, No. 4, July-August O Neil, T., Gilliatt, H., Strgana, T. W., Investigations of aeroelasti response for a system wit ontinuous strutural nonlinearities, AIAA, ASME, AHS, and ASC, 37 t, Strutures, Strutural Dynamis and Materials Conferene, Salt Lake City, UT, Apr. 18, 19, O Neil, T., Nonlinear aeroelasti response Analyses and Experiments, AIAA, Aerospae Sienes Meeting and Exibit, 34 t, Reno, NV, Jan 15-18, Beal, A., Marzoa, P., Rao, V. M., Gnann, A., Nonlinear Adaptive Control of an Aeroelasti Two- Dimensional Lifting Surfae, Journal of Guidane Control and Dynamis, Vol. 9, No., Mar-April Utturkar, Y., Holman, R., Mittal, R., Carroll, B., Seplak, M., Cattafesta L., A jet Formation Criterion for Synteti Jet Atuators, 41 st Aerospae Sienes Meeting & Exibit, 6-9 January 3/ Reno, NV.. Kersen, G., Lee, Y. S., Vakais, A. F., MFarland, D. M., Bergman, L. A., Irreversible Passive Energy Transfer in Coupled Osillators wit Essentials Nonlinearity, SIAM J. Appl Mat, Vol. 66, No, pp Lee, C., Hong, G., Ha, Q. P., Mallinson, S. G., A piezoeletrially atuated miro synteti jet for ative flow ontrol, Elsevier, Finale Paper aepted, 1 May 3.. MFarland, D. M., Kersen, G., Kowtko, J. J., Lee, Y. S., Bergman, L. A., Vakais, A. F., Experimental Investigation of targeted energy transfers in strongly and nonlinearly oupled osillators, J. Aoust. So. Am., 118(), August 5. 1

13 3. Traub, L. W., Miller, A., Rediniotis, O., Effets of Ative and Passive Flow Control on Dynami-Stall Vortex Formation, Journal of Airraft, Vol. 41, NO.: Engineering Notes. 4. Waszak, M., Modeling te Benmark Ative Control Tenology Wind-Tunnel Model for Appliation to Flutter Suppression, AIAA Paper No AIAA Atmosperi Fligt Meanis Conferene. San Diego, CA. July 9-31, Dowell, E.H., Edwards, J., and Strgana, T., Nonlinear Aeroelastiity, Journal of Airraft, Vol. 4, No. 5, 3, pp