Aeroelasticity
Aeroelasticity is the branch of
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:
- divergence where the aerodynamic forces increase the twist of a wing which further increases forces;
- control reversal where control activation produces an opposite aerodynamic moment that reduces, or in extreme cases reverses, the control effectiveness; and
- flutter which is uncontained vibration that can lead to the destruction of an aircraft.
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 and flight flutter trials. Flutter of control surfaces is usually eliminated by the careful placement of mass balances.
The synthesis of aeroelasticity with thermodynamics is known as aerothermoelasticity, and its synthesis with control theory is known as aeroservoelasticity.
History
The second failure of
In 1926, Hans Reissner published a theory of wing divergence, leading to much further theoretical research on the subject.[1] The term aeroelasticity itself was coined by Harold Roxbee Cox and Alfred Pugsley at the Royal Aircraft Establishment (RAE), Farnborough in the early 1930s.[2]
In the development of
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]
Static aeroelasticity
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 with ailerons 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
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 |
---|
Divergence can be understood as a simple property of the equation of motion is
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 where C is a coefficient, U is the free-stream fluid velocity, and α0 is the initial angle of attack. This yields an ordinary 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, 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 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 reversal
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 the Kaman servo-flap rotor design.[7]
Dynamic aeroelasticity
Dynamic aeroelasticity studies the interactions among aerodynamic, elastic, and inertial forces. Examples of dynamic aeroelastic phenomena are:
Flutter
Flutter is a dynamic instability of an elastic structure in a fluid flow, caused by
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 a Kármán 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 the
Aeroservoelasticity
In some cases, automatic control systems have been demonstrated to help prevent or limit flutter-related structural vibration.[12]
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
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.[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 the Langley Research Center.[16]
Buffeting
The methods for buffet detection are:
- Pressure coefficient diagram[17]
- Pressure divergence at trailing edge
- Computing separation from trailing edge based on Mach number
- Normal force fluctuating divergence
Prediction and cure
In the period 1950–1970, AGARD developed the Manual 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 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.
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 the p-method, the k-method and the p-k method.[7]
For nonlinear systems, flutter is usually interpreted as a limit cycle oscillation (LCO), and methods from the study of dynamical systems can be used to determine the speed at which flutter will occur.[19]
Media
These videos detail the
-
Time lapsed film of Active Aeroelastic Wing (AAW) Wing loads test, December, 2002
-
F/A-18A (now X-53) Active Aeroelastic Wing (AAW) flight test, December, 2002
Notable aeroelastic failures
- The original Tacoma Narrows Bridge was destroyed as a result of aeroelastic fluttering.[11]
- Propeller whirl flutter of the Braniff Flight 542.
- 1931 Transcontinental & Western Air Fokker F-10 crash.
- Body freedom flutter of the GAF Jindivik drone.[20]
See also
- Adaptive compliant wing
- Aerospace engineering
- Kármán vortex street
- Mathematical modeling
- Oscillation
- Parker Variable Wing
- Vortex shedding
- Vortex-induced vibration
- X-53 Active Aeroelastic Wing
References
- ^ ISBN 0-486-69189-6.
- ^ a b c "AeroSociety Podcast".
- ^ Theodore von Kármán (1967) The Wind and Beyond, page 155.
- ^ Ernest Edwin Sechler and L. G. Dunn (1942) Airplane Structural Analysis and Design from Internet Archive.
- OCLC 2295857.
- ^ Collar, A. R. (1978). "The first fifty years of aeroelasticity". Aerospace. 2. 5: 12–20.
- ^ ISBN 978-0-521-80698-5.
- ^ G. Dimitriadis, University of Liège, Aeroelasticity: Lecture 6: Flight testing.
- ^ "Binary Flutter as an Oscillating Windmill – Scaling & Linear Analysis". Wind Engineering. 37. 2013. Archived from the original on 2014-10-29.
- YouTube.
- ^ a b 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, "Resonance, Tacoma Bridge failure, and undergraduate physics textbooks"; Am. J. Phys. 59(2), 118–124, February 1991.
- ^ "Control of Aeroelastic Response: Taming the Threats" (PDF).
- ^ Reed, Wilmer H. (July 1967). "Review of propeller-rotor whirl flutter" (PDF). Nasa. Retrieved 2019-11-15.
- ^ "Lessons Learned From Civil Aviation Accidents". Retrieved 2019-12-14.
- doi:10.2514/3.57891.
- S2CID 120598336.
- S2CID 110673867.
- ^ "Manual on Aeroelasticity - Subject and author Index" (PDF). Archived from the original (PDF) on December 14, 2019. Retrieved 2019-12-14.
- .
- Defence Science and Technology Organisation. Archived(PDF) from the original on September 27, 2019.
Further reading
- Bisplinghoff, R. L., Ashley, H. and Halfman, H., Aeroelasticity. Dover Science, 1996, ISBN 0-486-69189-6, 880 p.
- Dowell, E. H., A Modern Course on Aeroelasticity. ISBN 90-286-0057-4.
- Fung, Y. C., An Introduction to the Theory of Aeroelasticity. Dover, 1994, ISBN 978-0-486-67871-9.
- Hodges, D. H. and Pierce, A., Introduction to Structural Dynamics and Aeroelasticity, Cambridge, 2002, ISBN 978-0-521-80698-5.
- Wright, J. R. and Cooper, J. E., Introduction to Aircraft Aeroelasticity and Loads, Wiley 2007, ISBN 978-0-470-85840-0.
- Hoque, M. E., "Active Flutter Control", ISBN 978-3-8383-6851-1.
- Collar, A. R., "The first fifty years of aeroelasticity", Aerospace, vol. 5, no. 2, pp. 12–20, 1978.
- Garrick, I. E. and Reed W. H., "Historical development of aircraft flutter", Journal of Aircraft, vol. 18, pp. 897–912, Nov. 1981.
- Patrick R. Veillette (Aug 23, 2018). "Low-Speed Buffet: High-Altitude, Transonic Training Weakness Continues". Business & Commercial Aviation. Aviation Week Network.