Aeroelasticity is the branch ofphysics andengineering studying the interactions between theinertial,elastic, andaerodynamic forces occurring while an elastic body is exposed to afluid flow. The study of aeroelasticity may be broadly classified into two fields:static aeroelasticity dealing with the static orsteady state response of an elastic body to a fluid flow, anddynamic aeroelasticity dealing with the body'sdynamic (typicallyvibrational) response.
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:
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,ground vibration tests andflight flutter trials. Flutter ofcontrol surfaces is usually eliminated by the careful placement ofmass balances.
The synthesis of aeroelasticity withthermodynamics is known asaerothermoelasticity, and its synthesis withcontrol theory is known asaeroservoelasticity.
The second failure ofSamuel Langley's prototype plane on the Potomac was attributed to aeroelastic effects (specifically,torsional divergence).[1] An early scientific work on the subject wasGeorge Bryan'sTheory of the Stability of a Rigid Aeroplane published in 1906.[2] Problems with torsional divergence plagued aircraft in theFirst World War 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 aHandley Page O/400 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 investigationF. W. Lanchester 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, theNational Physical Laboratory (NPL) was asked to investigate the phenomenon theoretically, which was subsequently carried out byLeonard Bairstow andArthur Fage.[2]
In 1926,Hans Reissner published a theory of wing divergence, leading to much further theoretical research on the subject.[1] The termaeroelasticity itself was coined byHarold Roxbee Cox andAlfred Pugsley at theRoyal Aircraft Establishment (RAE),Farnborough in the early 1930s.[2]
In the development ofaeronautical engineering atCaltech,Theodore von Kármán started a course "Elasticity applied to Aeronautics".[3] After teaching the course for one term, Kármán passed it over toErnest Edwin Sechler, who developed aeroelasticity in that course and in publication oftextbooks on the subject.[4][5]
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".[6]
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.Control reversal is a phenomenon occurring only in wings withailerons 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).
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 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.
| Equations for divergence of a simple beam |
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Divergence can be understood as a simple property of thedifferential equation(s) governing the wingdeflection. For example, modelling the airplane wing as anisotropicEuler–Bernoulli beam, the uncoupled torsionalequation of motion is wherey 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, andM’ is the aerodynamic moment per unit length. Under a simple lift forcing theory the aerodynamic moment is of the form whereC is a coefficient,U is the free-stream fluid velocity, and α0 is the initial angle of attack. This yields anordinary differential equation of the form where The boundary conditions for a clamped-free beam (i.e., a cantilever wing) are which yields the solution As can be seen, forλL =π/2 +nπ, with arbitrary integer numbern, 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 velocityU. 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.[7] |
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. Control reversal can be used to aerodynamic advantage, and forms part of theKaman servo-flap rotor design.[7]
Dynamic aeroelasticity studies the interactions among aerodynamic, elastic, and inertial forces. Examples of dynamic aeroelastic phenomena are:
Flutter is a dynamic instability of an elastic structure in a fluid flow, caused bypositive feedback between the body's deflection and the force exerted by the fluid flow. In alinear system, "flutter point" is the point at which the structure is undergoingsimple harmonic motion—zero netdamping—and so any further decrease in net damping will result in aself-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; andsoft flutter, in which the net damping decreases gradually.[8]
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.[9]
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 aKármán vortex street, which can induce structural oscillations.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 thestiffness 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,[10] as inNorthwest Airlines Flight 2 in 1938,Braniff Flight 542 in 1959, or the prototypes for Finland'sVL Myrsky fighter aircraft in the early 1940s. Famously, the originalTacoma Narrows Bridge was destroyed as a result of aeroelastic fluttering.[11]
In some cases, automatic control systems have been demonstrated to help prevent or limit flutter-related structural vibration.[12]
Propeller whirl flutter is a special case of flutter involving the aerodynamic and inertial effects of a rotating propeller and the stiffness of the supportingnacelle 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.[13] Failure of the engine supports led to whirl flutter occurring on two Lockheed L-188 Electra aircraft, in 1959 onBraniff Flight 542 and again in 1960 onNorthwest Orient Airlines Flight 710.[14]
Flow is highly non-linear in thetransonic 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 byHolt Ashley.[15] 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 theLangley Research Center.[16]
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. Generally it affects the tail unit of the aircraft structure due to air flow downstream of the wing.[citation needed]
The methods for buffet detection are:
In the period 1950–1970,AGARD developed theManual on Aeroelasticity which details the processes used in solving and verifying aeroelastic problems along with standard examples that can be used to test numerical solutions.[18]
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 amathematical model of the aircraft as a series of masses connected by springs and dampers which are tuned to represent thedynamic characteristics of the aircraft structure. The model also includes details of applied aerodynamic forces and how they vary.
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.
Methods of predicting flutter in linear structures include thep-method, thek-method and thep-k method.[7]
Fornonlinear systems, flutter is usually interpreted as alimit cycle oscillation (LCO), and methods from the study ofdynamical systems can be used to determine the speed at which flutter will occur.[19]
These videos detail theActive Aeroelastic Wing two-phaseNASA-Air Force flight research program to investigate the potential of aerodynamically twisting flexible wings to improve maneuverability of high-performance aircraft at transonic andsupersonic speeds, with traditional control surfaces such asailerons and leading-edge flaps used to induce the twist.
