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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 the aircraft or lead to its destruction, as
1108:
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. Generally it affects the tail unit of the aircraft structure due to air flow downstream of
1255:
285:
Divergence occurs when a lifting surface deflects under aerodynamic load in a direction which further increases lift in a positive feedback loop. The increased lift deflects the structure further, which eventually brings the structure to the point of divergence. Unlike flutter, which is another
924:
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-Bernoulli beam), control reversal speeds can be derived analytically as for torsional divergence.
906:. This is the torsional divergence 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 aerodynamic center) it is possible to eliminate the phenomenon of divergence altogether.
1238:
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structure. Dynamic instability can occur involving pitch and yaw degrees of freedom of the propeller and the engine supports leading to an unstable precession of the propeller. Failure of the engine supports led to whirl flutter occurring on two
Lockheed L-188 Electra aircraft, in 1959 on
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Structures exposed to aerodynamic forces—including wings and aerofoils, but also chimneys and bridges—are generally designed carefully within known parameters to avoid flutter. Blunt shapes, such as chimneys, can give off a continuous stream of vortices known as a
1236:
988:
980:
In water the mass ratio of the pitch inertia of the foil to that of the circumscribing cylinder of fluid is generally too low for binary flutter to occur, as shown by explicit solution of the simplest pitch and heave flutter stability determinant.
256:
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".
1167:
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.
182:
bomber during a flight in 1916, when it suffered a violent tail oscillation, which caused extreme distortion of the rear fuselage and the elevators to move asymmetrically. Although the aircraft landed safely, in the subsequent investigation
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In complex structures where both the aerodynamics and the mechanical properties of the structure are not fully understood, flutter can be discounted only through detailed testing. Even changing the mass distribution of an aircraft or the
602:
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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:
392:
987:
484:
187:
was consulted. One of his recommendations was that left and right elevators should be rigidly connected by a stiff shaft, which was to subsequently become a design requirement. In addition, the
666:
1156:
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
1235:
286:
aeroelastic problem, instead of irregular oscillations, divergence causes the lifting surface to move in the same direction and when it comes to point of divergence the structure deforms.
1081:. A phenomenon 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 of the
92:
Aircraft are prone to aeroelastic effects because they need to be lightweight while enduring large aerodynamic loads. Aircraft are designed to avoid the following aeroelastic problems:
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regime, dominated by moving shock waves. Avoiding flutter is mission-critical for aircraft that fly through transonic Mach numbers. The role of shock waves was first analyzed by
1540:
277:
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).
115:
Aeroelasticity problems can be prevented by adjusting the mass, stiffness or aerodynamics of structures which can be determined and verified through the use of calculations,
178:
and were solved largely by trial-and-error and ad hoc stiffening of the wing. The first recorded and documented case of flutter in an aircraft was that which occurred to a
1218:
flight research program to investigate the potential of aerodynamically twisting flexible wings to improve maneuverability of high-performance aircraft at transonic and
1586:
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,
1292:
926:
511:
1153:
which details the processes used in solving and verifying aeroelastic problems along with standard examples that can be used to test numerical solutions.
902:= 0 corresponds to the point of torsional divergence. For given structural parameters, this will correspond to a single value of free-stream velocity
1961:
677:
937:
Dynamic aeroelasticity studies the interactions among aerodynamic, elastic, and inertial forces. Examples of dynamic aeroelastic phenomena are:
196:
188:
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105:
where control activation produces an opposite aerodynamic moment that reduces, or in extreme cases reverses, the control effectiveness; and
1839:
1052:
is a special case of flutter involving the aerodynamic and inertial effects of a rotating propeller and the stiffness of the supporting
1956:
Garrick, I. E. and Reed W. H., "Historical development of aircraft flutter", Journal of
Aircraft, vol. 18, pp. 897–912, Nov. 1981.
1796:
Tang, D. M. (2004). "Effects of geometric structural nonlinearity on flutter and limit cycle oscillations of high-aspect-ratio wings".
269:
is a phenomenon in which the elastic twist of the wing suddenly becomes theoretically infinite, typically causing the wing to fail.
1843:
1765:
1041:
In some cases, automatic control systems have been demonstrated to help prevent or limit flutter-related structural vibration.
1989:
1730:
Golestani, A.; et al. (2015). "An experimental study of buffet detection on supercritical airfoils in transonic regime".
1947:
1932:
1917:
1902:
1512:
1062:
323:
613:
241:
started a course "Elasticity applied to
Aeronautics". After teaching the course for one term, Kármán passed it over to
417:’ is the aerodynamic moment per unit length. Under a simple lift forcing theory the aerodynamic moment is of the form
1887:
1872:
1386:
423:
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Farmer, M. G.; Hanson, P. W. (1976). "Comparison of Super-critical and
Conventional Wing Flutter Characteristics".
1939:
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502:
211:
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published a theory of wing divergence, leading to much further theoretical research on the subject. The term
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of the aircraft structure. The model also includes details of applied aerodynamic forces and how they vary.
1994:
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1207:
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219:
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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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2004:
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of the aircraft as a series of masses connected by springs and dampers which are tuned to represent the
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191:(NPL) was asked to investigate the phenomenon theoretically, which was subsequently carried out by
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Proceedings of the
Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering
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35:
2019:
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597:{\displaystyle {\frac {d^{2}\theta }{dy^{2}}}+\lambda ^{2}\theta =-\lambda ^{2}\alpha _{0},}
1805:
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1338:
1005:
242:
82:
58:
8:
1161:
973:, in which the net damping decreases very suddenly, very close to the flutter point; and
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where the aerodynamic forces increase the twist of a wing which further increases forces;
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162:'s prototype plane on the Potomac was attributed to aeroelastic effects (specifically,
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192:
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Ashley, Holt (1980). "Role of Shocks in the 'Sub-Transonic' Flutter
Phenomenon".
1343:
1245:
Time lapsed film of Active
Aeroelastic Wing (AAW) Wing loads test, December, 2002
995:
Video of the Tacoma
Narrows Bridge being destroyed through aeroelastic fluttering
167:
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are typically wrapped around chimneys to stop the formation of these vortices.
215:
159:
143:
135:
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which is uncontained vibration that can lead to the destruction of an aircraft.
54:
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The boundary conditions for a clamped-free beam (i.e., a cantilever wing) are
174:
published in 1906. Problems with torsional divergence plagued aircraft in the
2013:
1743:
1407:
961:
953:
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Control reversal can be used to aerodynamic advantage, and forms part of the
203:
69:
flow. The study of aeroelasticity may be broadly classified into two fields:
1707:
1263:
F/A-18A (now X-53) Active
Aeroelastic Wing (AAW) flight test, December, 2002
952:
between the body's deflection and the force exerted by the fluid flow. In a
948:
is a dynamic instability of an elastic structure in a fluid flow, caused by
1541:"Binary Flutter as an Oscillating Windmill – Scaling & Linear Analysis"
1466:
1299:
757:{\displaystyle \theta |_{y=0}=\left.{\frac {d\theta }{dy}}\right|_{y=L}=0,}
74:
1137:
1333:
1191:
1123:
1078:
175:
50:
1962:"Low-Speed Buffet: High-Altitude, Transonic Training Weakness Continues"
1698:
1979:
1588:"Resonance, Tacoma Bridge failure, and undergraduate physics textbooks"
1219:
1097:
Buffeting of the fin caused by the breakdown of the vortex on the NASA
265:
In an aeroplane, two significant static aeroelastic effects may occur.
30:
1074:
1026:
1013:
307:
163:
86:
1675:
956:, "flutter point" is the point at which the structure is undergoing
245:, who developed aeroelasticity in that course and in publication of
246:
1480:
Collar, A. R. (1978). "The first fifty years of aeroelasticity".
1223:
1141:
Mass balances protruding from an aileron used to suppress flutter
1053:
274:
234:
46:
1198:
can be used to determine the speed at which flutter will occur.
1171:
Methods of predicting flutter in linear structures include the
1567:
Visual demonstration of flutter which destroys an RC aircraft
1146:
964:—and so any further decrease in net damping will result in a
66:
1029:
fighter aircraft in the early 1940s. Famously, the original
27:
Interactions among inertial, elastic, and aerodynamic forces
1211:
707:
1984:
1833:
Aircraft Accident Investigation at ARL-The first 50 years
1376:
1293:
1931 Transcontinental & Western Air Fokker F-10 crash
298:
Divergence can be understood as a simple property of the
166:
divergence). An early scientific work on the subject was
65:
forces occurring while an elastic body is exposed to a
1910:
Introduction to Structural Dynamics and Aeroelasticity
1505:
Introduction to Structural Dynamics and Aeroelasticity
2000:
NACA Technical Reports – NASA Langley Research Center
1766:"Manual on Aeroelasticity - Subject and author Index"
1729:
1601:"Control of Aeroelastic Response: Taming the Threats"
1377:
Bisplinghoff, R. L.; Ashley, H.; Halfman, H. (1996).
1033:
was destroyed as a result of aeroelastic fluttering.
776:
680:
616:
514:
426:
387:{\displaystyle GJ{\frac {d^{2}\theta }{dy^{2}}}=-M',}
326:
1980:
Aeroelasticity Branch – NASA Langley Research Center
1959:
1278:
was destroyed as a result of aeroelastic fluttering.
1995:
The Aeroelasticity Group – Texas A&M University
1222:speeds, with traditional control surfaces such as
867:
756:
661:{\displaystyle \lambda ^{2}=C{\frac {U^{2}}{GJ}}.}
660:
596:
478:
386:
127:is usually eliminated by the careful placement of
1925:Introduction to Aircraft Aeroelasticity and Loads
1863:Bisplinghoff, R. L., Ashley, H. and Halfman, H.,
1226:and leading-edge flaps used to induce the twist.
1194:oscillation (LCO), and methods from the study of
1122:Computing separation from trailing edge based on
306:. For example, modelling the airplane wing as an
77:response of an elastic body to a fluid flow, and
2011:
1402:
1400:
1398:
977:, in which the net damping decreases gradually.
1895:An Introduction to the Theory of Aeroelasticity
1643:"Lessons Learned From Civil Aviation Accidents"
1268:
501:is the initial angle of attack. This yields an
479:{\displaystyle M'=CU^{2}(\theta +\alpha _{0}),}
1372:
1370:
1590:; Am. J. Phys. 59(2), 118–124, February 1991.
1395:
273:is a phenomenon occurring only in wings with
1688:
1533:
1004:, which can induce structural oscillations.
172:Theory of the Stability of a Rigid Aeroplane
1840:Defence Science and Technology Organisation
1582:
1580:
1367:
1068:
1044:
292:Equations for divergence of a simple beam
1706:
1619:"Review of propeller-rotor whirl flutter"
1527:Aeroelasticity: Lecture 6: Flight testing
1025:in 1959, or the prototypes for Finland's
932:
1938:Hoque, M. E., "Active Flutter Control",
1849:from the original on September 27, 2019.
1577:
1499:
1497:
1495:
1136:
1092:
983:
497:is the free-stream fluid velocity, and α
409:is the torsional stiffness of the beam,
260:
29:
1559:
1456:
1441:Airplane Structural Analysis and Design
14:
2012:
1830:
1661:
1479:
1190:, flutter is usually interpreted as a
1132:
1112:The methods for buffet detection are:
1036:
53:studying the interactions between the
1960:Patrick R. Veillette (Aug 23, 2018).
1524:G. Dimitriadis, University of Liège,
1492:
134:The synthesis of aeroelasticity with
1795:
1616:
1119:Pressure divergence at trailing edge
1063:Northwest Orient Airlines Flight 710
868:{\displaystyle \theta =\alpha _{0}.}
1818:10.1016/j.jfluidstructs.2003.10.007
1503:Hodges, D. H. and Pierce, A.,
1128:Normal force fluctuating divergence
913:
24:
1966:Business & Commercial Aviation
1857:
405:is the elastic twist of the beam,
25:
2051:
1973:
1923:Wright, J. R. and Cooper, J. E.,
1880:A Modern Course on Aeroelasticity
1073:Flow is highly non-linear in the
1250:
1231:
890:, with arbitrary integer number
1985:DLR Institute of Aeroelasticity
1940:LAP Lambert Academic Publishing
1824:
1789:
1758:
1723:
1682:
1655:
1635:
1610:
1593:
1281:Propeller whirl flutter of the
1908:Hodges, D. H. and Pierce, A.,
1798:Smart Materials and Structures
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1473:
1450:
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1414:
859:
850:
841:
829:
820:
811:
802:
793:
686:
503:ordinary differential equation
470:
451:
13:
1:
1990:National Aerospace Laboratory
1617:Reed, Wilmer H. (July 1967).
1360:
280:
2005:NASA Aeroelasticity Handbook
1354:X-53 Active Aeroelastic Wing
1298:Body freedom flutter of the
1269:Notable aeroelastic failures
1116:Pressure coefficient diagram
1088:
220:Royal Aircraft Establishment
189:National Physical Laboratory
38:in a wind tunnel for flutter
7:
1306:
1019:Northwest Airlines Flight 2
401:is the spanwise dimension,
73:dealing with the static or
34:NASA testing a scale model
10:
2056:
940:
917:
767:which yields the solution
313:, the uncoupled torsional
153:
1461:. New York: McGraw-Hill.
1459:Elasticity in Engineering
1145:In the period 1950–1970,
142:, and its synthesis with
1968:. Aviation Week Network.
1744:10.1177/0954410014531743
1349:Vortex-induced vibration
1206:These videos detail the
1201:
1151:Manual on Aeroelasticity
1069:Transonic aeroelasticity
413:is the beam length, and
231:aeronautical engineering
81:dealing with the body's
1867:. Dover Science, 1996,
1457:Sechler, E. E. (1952).
1314:Adaptive compliant wing
1208:Active Aeroelastic Wing
1162:dynamic characteristics
1083:Langley Research Center
1050:Propeller whirl flutter
1045:Propeller whirl flutter
302:(s) governing the wing
1831:Kepert, J. L. (1993).
1551:. 2013. Archived from
1439:and L. G. Dunn (1942)
1283:Lockheed L-188 Electra
1142:
1102:
996:
958:simple harmonic motion
933:Dynamic aeroelasticity
927:Kaman servo-flap rotor
869:
758:
662:
598:
480:
388:
254:Arthur Roderick Collar
229:In the development of
158:The second failure of
117:ground vibration tests
79:dynamic aeroelasticity
39:
2030:Aerospace engineering
1408:"AeroSociety Podcast"
1329:Mathematical modeling
1319:Aerospace engineering
1276:Tacoma Narrows Bridge
1140:
1096:
1061:and again in 1960 on
1031:Tacoma Narrows Bridge
994:
870:
759:
663:
599:
481:
389:
300:differential equation
261:Static aeroelasticity
210:itself was coined by
121:flight flutter trials
71:static aeroelasticity
33:
2040:Elasticity (physics)
2025:Aircraft wing design
1778:on December 14, 2019
1437:Ernest Edwin Sechler
1339:Parker Variable Wing
1324:Kármán vortex street
1002:Kármán vortex street
878:As can be seen, for
774:
678:
614:
512:
424:
324:
311:Euler–Bernoulli beam
243:Ernest Edwin Sechler
226:in the early 1930s.
140:aerothermoelasticity
1912:, Cambridge, 2002,
1810:2004JFS....19..291T
1699:10.2514/6.1976-1560
1664:Journal of Aircraft
1507:, Cambridge, 2002,
1425:The Wind and Beyond
1421:Theodore von Kármán
1133:Prediction and cure
1037:Aeroservoelasticity
239:Theodore von Kármán
148:aeroservoelasticity
1287:Braniff Flight 542
1158:mathematical model
1143:
1103:
1059:Braniff Flight 542
1023:Braniff Flight 542
997:
865:
754:
658:
594:
493:is a coefficient,
476:
384:
315:equation of motion
180:Handley Page O/400
40:
1948:978-3-8383-6851-1
1942:, Germany, 2010,
1933:978-0-470-85840-0
1918:978-0-521-80698-5
1903:978-0-486-67871-9
1513:978-0-521-80698-5
1381:. Dover Science.
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1240:
1196:dynamical systems
1188:nonlinear systems
992:
950:positive feedback
911:
910:
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212:Harold Roxbee Cox
45:is the branch of
16:(Redirected from
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1848:
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1771:. Archived from
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1710:
1708:2060/19760015071
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1445:Internet Archive
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920:Control reversal
914:Control reversal
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271:Control reversal
249:on the subject.
193:Leonard Bairstow
185:F. W. Lanchester
125:control surfaces
103:control reversal
36:Lockheed Electra
21:
2055:
2054:
2050:
2049:
2048:
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2045:
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2035:Solid mechanics
2010:
2009:
1976:
1897:. Dover, 1994,
1878:Dowell, E. H.,
1860:
1858:Further reading
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1974:External links
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1927:, Wiley 2007,
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1865:Aeroelasticity
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1856:
1853:
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1823:
1804:(3): 291–306.
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1738:(2): 312–322.
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1670:(3): 187–197.
1654:
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1555:on 2014-10-29.
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1379:Aeroelasticity
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136:thermodynamics
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43:Aeroelasticity
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2020:Aerodynamics
1965:
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1780:. Retrieved
1773:the original
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1553:the original
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78:
75:steady state
70:
42:
41:
1427:, page 155.
1334:Oscillation
1192:limit cycle
1124:Mach number
1101:F/A-18 wing
1079:Holt Ashley
224:Farnborough
197:Arthur Fage
87:vibrational
85:(typically
63:aerodynamic
51:engineering
2014:Categories
1838:(Report).
1782:2019-12-14
1648:2019-12-14
1628:2019-11-15
1361:References
1220:supersonic
1210:two-phase
1181:p-k method
1109:the wing.
960:—zero net
304:deflection
281:Divergence
267:Divergence
97:divergence
1752:110673867
1717:120598336
1482:Aerospace
1216:Air Force
1106:Buffeting
1089:Buffeting
1075:transonic
1027:VL Myrsky
1021:in 1938,
1014:stiffness
854:−
845:λ
839:
824:λ
818:
806:λ
800:
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529:θ
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455:θ
371:−
347:θ
308:isotropic
252:In 1947,
247:textbooks
202:In 1926,
164:torsional
18:Buffeting
1875:, 880 p.
1844:Archived
1488:: 12–20.
1307:See also
1224:ailerons
1179:and the
1177:k-method
1173:p-method
929:design.
432:′
378:′
275:ailerons
55:inertial
1806:Bibcode
1572:YouTube
1467:2295857
1423:(1967)
1054:nacelle
1006:Strakes
962:damping
946:Flutter
941:Flutter
235:Caltech
222:(RAE),
218:at the
154:History
109:flutter
83:dynamic
59:elastic
47:physics
1946:
1931:
1916:
1901:
1886:
1871:
1750:
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1175:, the
894:, tan(
607:where
489:where
397:where
61:, and
1847:(PDF)
1836:(PDF)
1776:(PDF)
1769:(PDF)
1748:S2CID
1713:S2CID
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1484:. 2.
1443:from
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1147:AGARD
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67:fluid
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1914:ISBN
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1884:ISBN
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1463:OCLC
1383:ISBN
1212:NASA
1186:For
1099:HARV
214:and
195:and
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317:is
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