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| '''Aeroelasticity''' is the branch of [[physics]] and [[engineering]] that studies the interactions between the [[inertial force|inertial]], [[elasticity (physics)|elastic]], and [[aerodynamic force|aerodynamic]] forces that occur when an elastic body is exposed to a [[fluid]] flow. Although historical studies have been focused on aeronautical applications, recent research has found applications in fields such as [[energy harvesting]] <ref>{{cite journal|last=Sousa|first=V. C.|title=Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities: theory and experiment|journal=Smart Materials and Structures|year=2011|volume=20|number=9}}</ref> and understanding [[snoring]].<ref>{{cite journal|last=Ellis|first= P. D. M. |title= Laser palatoplasty for snoring due to palatal flutter: a further report|journal= Clinical Otolaryngology|year=1994|volume=19|number=4}}</ref> The study of aeroelasticity may be broadly classified into two fields: static aeroelasticity, which deals with the static or [[steady state|steady]] response of an elastic body to a fluid flow; and dynamic aeroelasticity, which deals with the body’s [[Dynamics (mechanics)|dynamic]] (typically [[vibration]]al) response. Aeroelasticity draws on the study of [[fluid mechanics]], [[solid mechanics]], [[structural dynamics]] and [[dynamical systems]].
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| The synthesis of aeroelasticity with [[thermodynamics]] is known as [[aerothermoelasticity]], and its synthesis with [[control theory]] is known as [[aeroservoelasticity]].
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| == History ==
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| The 2nd failure of [[Samuel Langley]]'s prototype plane on the Potomac has been attributed to aeroelastic effects (specifically, torsional divergence).<ref name="Bisplinghoff">Bisplinghoff, R.L., Ashley, H. and Halfman, H., ''Aeroelasticity''. Dover Science, 1996, ISBN 0-486-69189-6</ref> Problems with torsional divergence plagued aircraft in the First World War, and were solved largely by trial-and-error and ad-hoc stiffening of the wing. In 1926 [[Hans Reissner]] published a theory of wing divergence, leading to much further theoretical research on the subject.<ref name="Bisplinghoff" /> In 1947 [[Arthur Roderick Collar]] defined aeroelasticity as ''"the study of the mutual interaction that takes place within the triangle of the inertial, elastic, and aerodynamic forces acting on structural members exposed to an airstream, and the influence of this study on design."''<ref>{{cite journal|last=Collar|first=A. R.|title=The first fifty years of aeroelasticity|journal=Aerospace|year=1978|volume=5|series=2|pages=12–20}}</ref>
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| == Static aeroelasticity ==
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| In an aeroplane, two significant static aeroelastic effects may occur. ''Divergence'' is a phenomenon in which the elastic twist of the wing suddenly becomes theoretically infinite, typically causing the wing to fail spectacularly. ''Control reversal'' is a phenomenon occurring only in wings with [[aileron]]s or other control surfaces, in which these control surfaces reverse their usual functionality (e.g. the rolling direction associated with a given aileron moment is reversed).
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| === Divergence ===
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| Divergence occurs when a lifting surface deflects under aerodynamic load so as to increase the applied load, or move the load so that the twisting effect on the structure is increased. The increased load deflects the structure further, which eventually brings the structure to the diverge point. Divergence can be understood as a simple property of the [[differential equation]](s) governing the wing [[deflection (engineering)|deflection]]. For example, modelling the aeroplane wing as an [[isotropic]] [[Euler–Bernoulli beam theory|Euler–Bernoulli beam]], the uncoupled torsional [[equation of motion]] is:
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| : <math> GJ \frac{d^2 \theta}{dy^2} = -M'</math>
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| Where ''y'' is the spanwise dimension, ''θ'' is the elastic twist of the beam, ''GJ'' is the torsional stiffness of the beam, ''L'' is the beam length, and ''M’'' is the aerodynamic moment per unit length. Under a simple lift forcing theory the aerodynamic moment is of the form:
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| : <math>M' = C U^2 (\theta + \alpha_0) </math>
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| Where ''C'' is a coefficient, ''U'' is the free-stream fluid velocity, and α<sub>0</sub> is the initial angle of attack. This yields an [[ordinary differential equation]] of the form:
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| : <math> \frac{d^2 \theta}{dy^2} + \lambda^2 \theta = -\lambda^2 \alpha_0 </math>
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| Where:
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| : <math> \lambda^2 = C/(GJ)</math>
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| The boundary conditions for a clamped-free beam (i.e. a cantilever wing) are:
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| : <math> \theta|_{y=0} = \frac{d\theta}{dy}\biggl|_{y=L} = 0</math>
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| Which yields the solution:
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| : <math> \theta = \alpha_{0} [\tan (\lambda L) \sin(\lambda y) + \cos (\lambda y) - 1]</math>
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| As can be seen, for ''λL = π/2 + nπ'', with arbitrary integer number ''n'', ''tan(λL)'' is infinite. ''n = 0'' corresponds to the point of torsional divergence. For given structural parameters, this will correspond to a single value of free-stream velocity U. This is the torsional diverengence speed. Note that for some special boundary conditions that may be implemented in a wind tunnel test of an airfoil (e.g. a torsional restraint positioned forward of the centre of lift) it is possible to eliminate the phenomenon of divergence altogether.
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| <ref name="Hodges">Hodges, D.H. and Pierce, A., ''Introduction to Structural Dynamics and Aeroelasticity'', Cambridge, 2002, ISBN 978-0-521-80698-5</ref>
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| === Control reversal ===
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| {{main|Control reversal}}
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| Control surface reversal is the loss (or reversal) of the expected response of a control surface, due to deformation of the main lifting surface. For simple models (e.g. single aileron on an Euler-Benouilli beam), control reversal speeds can be derived analytically as for torsional divergence. Control reversal can be used to an aerodynamic advantage, and forms part of the [[Kaman servo-flap rotor]] design.<ref name="Hodges" />
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| == Dynamic aeroelasticity ==
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| '''Dynamic Aeroelasticity''' studies the interactions among aerodynamic, elastic, and inertial forces. Examples of dynamic aeroelastic phenomena are:
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| === Flutter ===<!-- This section is linked from [[Resonance]], and [[Aeroelastic flutter]] redirects here -->
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| '''Flutter''' is a dynamic instability of an elastic structure in a fluid flow, caused by [[positive feedback]] between the body's deflection and the forcing exerted by the fluid flow. In a [[linear system]] 'flutter point' is the point at which the structure is undergoing [[simple harmonic motion]] - zero net [[damping]] - and so any further decrease in net damping will result in a [[self-oscillation]] and eventual failure. 'Net damping' can be understood as the sum of the structure's natural positive damping, and the negative damping of the aerodynamic force. Flutter can be classified into two types: ''hard flutter'', in which the net damping decreases very suddenly, very close to the flutter point; and ''soft flutter'', in which the net damping decreases gradually.<ref>G. Dimitriadis, University of Liège, ''Aeroelasticity: Lectrue 6: Flight testing'', [http://www.ltas-aea.ulg.ac.be/cms/uploads/Aeroelasticity06.pdf]</ref> Methods of predicting flutter in linear structures include the [[p-method]], the [[k-method]] and the [[p-k method]].<ref name="Hodges" />
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| For [[nonlinear system]]s, flutter is usually interpreted as a [[limit cycle]] oscillation (LCO), and methods from the study of [[dynamical system]]s can be used to determine the speed at which flutter will occur.<ref>{{cite journal|last=Tang|first=D. M.|title=Effects of geometric structural nonlinearity on flutter and limit cycle oscillations of high-aspect-ratio wings|journal=Smart Materials and Structures|year=2004|volume=19}}</ref>
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| Structures exposed to aerodynamic forces — including wings and aerofoils, but also chimneys and bridges — are designed carefully within known parameters to avoid flutter. In complex structures where both the aerodynamics and the mechanical properties of the structure are not fully understood, flutter can only be discounted through detailed testing. Even changing the mass distribution of an aircraft or the [[stiffness]] of one component can induce flutter in an apparently unrelated aerodynamic component. At its mildest this can appear as a "[[buzz]]" in the aircraft structure, but at its most violent it can develop uncontrollably with great speed and cause serious damage to or lead to the destruction of the aircraft,<ref name = "YouTube">{{citation | format = Video | publisher = Google | title = YouTube | url = http://www.youtube.com/watch?v=nRit6tcNT4s | contribution = Visual demonstration of flutter which destroys an RC aircraft}}.</ref> as in [[Braniff Flight 542]].
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| In some cases, automatic control systems have been demonstrated to help prevent or limit flutter-related structural vibration.<ref>http://history.nasa.gov/monograph39/mon39_b.pdf</ref>
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| Flutter can also occur on structures other than aircraft. One famous example of flutter phenomena is the collapse of the original [[Tacoma Narrows Bridge (1940)|Tacoma Narrows Bridge]].<ref>The adequacy of comparison between flutter in aircraft aerodynamics and Tacoma Narrows Bridge case is discussed and disputed in Yusuf K. Billah, Robert H. Scanian, [http://www.ketchum.org/billah/Billah-Scanlan.pdf "Resonance, Tacoma Bridge failure, and undergraduate physics textbooks"]; Am. J. Phys. 59, nr 2, s. 118-124, February 1991</ref>
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| Flutter as a [[controlled aerodynamic instability phenomena|controlled aerodynamic instability phenomenon]] is used intentionally and positively in wind mills for generating electricity and in other works like making musical tones on ground-mounted devices, as well as on [[Kite types|musical kites]]. Flutter is not always a destructive force; recent progress has been made in small scale (table top) wind generators for underserved communities in developing countries, designed specifically to take advantage of this effect.<ref>{{cite web |url=http://www.popularmechanics.com/technology/industry/4224763.html?series=37 | title = Windbelt, Cheap Generator Alternative, Set to Power Third World | publisher = Popular Mechanics}}</ref><ref>{{citation | publisher = Humdinger Wind Energy | url = http://www.humdingerwind.com/windbelt.html | title = Windbelt technology}}.</ref> Peter Allan Sharp (of Oakland, California) and Jonathan Hare (of University of Sussex) demonstrated, in March 2007, a linear generator run by two flutter wings.<ref>{{citation | publisher = Creative Science | place = UK | url = http://www.creative-science.org.uk/sharp_flutter.html | title = FlutterMill}}.</ref> The wind energy industry distinguishes between flutter wings, flip wings, and oscillating tensionally-held sweeping membrane wings for wind milling.<ref>{{citation | publisher = Energy kite systems | url = http://www.energykitesystems.net/FlexorEnergy/ | title = Flexor Energy Company}}.</ref>
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| === Buffeting ===
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| '''Buffeting''' is a high-frequency instability, caused by airflow separation or shock wave oscillations from one object striking another. It is caused by a sudden impulse of load increasing. It is a random forced vibration.
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| Generally it affects the tail unit of the aircraft structure due to air flow downstream of the wing.
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| === Transonic Aeroelasticity===
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| Flow is highly non-linear in the [[transonic]] regime, dominated by moving shock waves. It is mission-critical for aircraft that fly through transonic Mach numbers. The role of shock waves was first analyzed by [[Holt Ashley]].<ref>Holt Ashley. "Role of Shocks in the "Sub-Transonic" Flutter Phenomenon", Journal of Aircraft, Vol. 17, No. 3 (1980), pp. 187-197.</ref> A phenenenon that impacts stability of aircraft known as 'transonic dip', in which the flutter speed can get close to flight speed, was reported in May 1976 by Farmer and Hanson <ref>Farmer, M.G. and Hanson, P.W., “Comparison of Super-
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| critical and Conventional Wing Flutter Characteristics,” NASA TM X-
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| 72837</ref> of the [[Langley Research Center]].
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| == Prediction and cure ==
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| Aeroelasticity involves not just the external aerodynamic loads and the way they change but also the structural, [[damping]] and mass characteristics of the aircraft. Prediction involves making a [[mathematical model]] of the aircraft as a series of masses connected by springs and dampers which are tuned to represent the [[dynamic characteristics]] of the aircraft structure. The model also includes details of applied aerodynamic forces and how they vary.
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| The model can be used to predict the flutter margin and, if necessary, test fixes to potential problems. Small carefully chosen changes to mass distribution and local structural stiffness can be very effective in solving aeroelastic problems.
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| == Media ==
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| These videos detail the [[X-53 Active Aeroelastic Wing|Active Aeroelastic Wing]] two-phase [[NASA]]-[[United States Air Force|Air Force]] flight research program to investigate the potential of aerodynamically twisting flexible wings to improve maneuverability of high-performance aircraft at transonic and [[supersonic]] speeds, with traditional control surfaces such as [[aileron]]s and leading-edge flaps used to induce the twist.
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| <gallery>
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| Image:Active Aeroelastic Wing time lapse.ogg|Time lapsed film of Active Aeroelastic Wing (AAW) Wing loads test, December, 2002
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| Image:F-18A Active Aeroelastic Wing flight test.ogg|F/A-18A (now X-53) Active Aeroelastic Wing (AAW) flight test, December, 2002
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| </gallery>
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| == See also ==
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| {{multicol}}
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| *[[Adaptive Compliant Wing]]
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| *[[Aerospace engineering]]
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| * [[Flutter (electronics and communication)]]
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| *[[Kármán vortex street]]
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| *[[Mathematical modeling]]
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| *[[Oscillation]]
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| {{multicol-break}}
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| *[[Parker Variable Wing]]
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| *[[Tacoma Narrows Bridge (1940)]]
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| *[[TWA Flight 599]]
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| *[[Vortex-induced vibration]]
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| *[[Vortex shedding]]
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| *[[X-53 Active Aeroelastic Wing]]
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| {{multicol-end}}
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| == References ==
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| <references/>
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| == Further reading ==
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| *Bisplinghoff, R.L., Ashley, H. and Halfman, H., ''Aeroelasticity''. Dover Science, 1996, ISBN 0-486-69189-6, 880 pgs;
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| *Dowell, E. H., ''A Modern Course on Aeroelasticity''. ISBN 90-286-0057-4;
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| *Fung, Y.C., ''An Introduction to the Theory of Aeroelasticity''. Dover, 1994, ISBN 978-0-486-67871-9;
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| *Hodges, D.H. and Pierce, A., ''Introduction to Structural Dynamics and Aeroelasticity'', Cambridge, 2002, ISBN 978-0-521-80698-5;
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| *Wright, J.R. and Cooper, J.E., ''Introduction to Aircraft Aeroelasticity and Loads'', Wiley 2007, ISBN 978-0-470-85840-0.
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| *Hoque, M. E., "Active Flutter Control", [[LAP Lambert Academic Publishing]], Germany, 2010, ISBN 978-3-8383-6851-1.
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| *Collar, A. R., "The first fifty years of aeroelasticity," Aerospace, vol. 5, no. 2, pp. 12–20, 1978
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| *Garrick, I.E. and Reed W.H., "Historical development of aircraft flutter," Journal of Aircraft, vol. 18, pp. 897–912, Nov. 1981.
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| == External links ==
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| *[http://aeroelasticity.larc.nasa.gov/ Aeroelasticity Branch - NASA Langley Research Center]
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| *[http://www.dlr.de/ae/en DLR Institute of Aeroelasticity]
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| *[http://www.nlr.nl/smartsite.dws?l=en&id=9041 National Aerospace Laboratory]
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| *[http://aeweb.tamu.edu/aeroel/ The Aeroelasticity Group - Texas A&M University]
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| *[http://naca.larc.nasa.gov/ NACA Technical Reports - NASA Langley Research Center]
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| [[Category:Aerodynamics]]
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| [[Category:Aircraft wing design]]
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| [[Category:Aerospace engineering]]
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| [[Category:Solid mechanics]]
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| [[Category:Elasticity (physics)]]
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| [[Category:Articles containing video clips]]
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