Editing Aeroelasticity (section)

=== Flutter ===<!-- This section is linked from [[Resonance]], and [[Aeroelastic flutter]] redirects here -->
'''Flutter''' is a dynamic instability of an elastic structure in a fluid flow, caused by [[positive feedback]] between the body's deflection and the force 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 ratio|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, [http://www.ltas-aea.ulg.ac.be/cms/uploads/Aeroelasticity06.pdf ''Aeroelasticity: Lecture 6: Flight testing''].</ref>

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.<ref name="windeng372013">{{cite journal |url=http://multi-science.metapress.com/content/c553k773504m276x/?p=b99b20fe0d14408b9a01c901c4c31c05&pi=3 |archive-url=https://archive.today/20141029011643/http://multi-science.metapress.com/content/c553k773504m276x/?p=b99b20fe0d14408b9a01c901c4c31c05&pi=3 |url-status=dead |archive-date=2014-10-29 |title=Binary Flutter as an Oscillating Windmill – Scaling & Linear Analysis |journal=Wind Engineering |volume=37 |year=2013 }}</ref>

[[File:Tacoma Narrows Bridge destruction.ogv|thumb|Video of the Tacoma Narrows Bridge being destroyed through aeroelastic fluttering]]
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 [[Kármán vortex street]], which can induce structural oscillations. [[Strake (aeronautics)|Strakes]] are typically wrapped around chimneys to stop the formation of these vortices.

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 [[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 the aircraft or lead to its destruction,<ref name = "YouTube">{{YouTube|nRit6tcNT4s|Visual demonstration of flutter which destroys an RC aircraft}}.</ref> as in [[Northwest Airlines Flight 2]] in 1938, [[Braniff Flight 542]] in 1959, or the prototypes for Finland's [[VL Myrsky]] fighter aircraft in the early 1940s. Famously, the original [[Tacoma Narrows Bridge (1940)|Tacoma Narrows Bridge]] was destroyed as a result of aeroelastic fluttering.<ref name="billah91">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(2), 118–124, February 1991.</ref>

==== Aeroservoelasticity ====
In some cases, automatic control systems have been demonstrated to help prevent or limit flutter-related structural vibration.<ref>{{cite web |url=https://history.nasa.gov/monograph39/mon39_b.pdf |title=Control of Aeroelastic Response: Taming the Threats }}</ref>

==== Propeller whirl flutter ====
''Propeller whirl flutter'' is a special case of flutter involving the aerodynamic and inertial effects of a rotating propeller and the stiffness of the supporting [[nacelle]] 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.<ref>{{cite web |url=https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19670020798.pdf |first=Wilmer H. |last=Reed |title=Review of propeller-rotor whirl flutter |date=July 1967 |publisher=Nasa |access-date=2019-11-15}}</ref> Failure of the engine supports led to whirl flutter occurring on two Lockheed L-188 Electra aircraft, in 1959 on [[Braniff Flight 542]] and again in 1960 on [[Northwest Orient Airlines Flight 710]].<ref>{{cite web |title=Lessons Learned From Civil Aviation Accidents |url=https://lessonslearned.faa.gov/ll_main.cfm?TabID=2&LLID=7&LLTypeID=2 |access-date=2019-12-14}}</ref>

==== Transonic aeroelasticity ====
Flow is highly non-linear in the [[transonic]] 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 [[Holt Ashley]].<ref>{{cite journal |first=Holt |last=Ashley |title=Role of Shocks in the 'Sub-Transonic' Flutter Phenomenon |journal=Journal of Aircraft |volume=17 |issue=3 |year=1980 |pages=187–197 |doi=10.2514/3.57891 }}</ref> 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 [[Langley Research Center]].<ref>{{cite journal |last1=Farmer |first1=M. G. |last2=Hanson |first2=P. W. |title=Comparison of Super-critical and Conventional Wing Flutter Characteristics |journal=NASA Tm X-72837 |date=1976 |doi=10.2514/6.1976-1560 |hdl=2060/19760015071 |s2cid=120598336 |hdl-access=free }}</ref>