AEROELASTICITY

Aeroelastic triangle of forces or Collar’s triangle : The term Aeroelasticity has been applied by Aeronautical engineers to an important class of problems in air plane design. It is often defined as a science which studies the mutual interaction between aerodynamic forces and elastic forces and the influence of the interaction of these forces on air plane design. Aeroelastic problems would not exist if air plane structures were perfectly rigid. Modern air plane structures are very flexible and, and this flexibility is fundamentally responsible for the various aeroelastic phenomena.

Structural flexibility itself may not be objectionable; however aeroelastic phenomena arise when structural deformations induce additional aerodynamic forces. These additional aerodynamic forces may produce additional structural deformations which will induce greater aerodynamic forces. Such interactions may tend to become smaller and smaller until a condition of stable equilibrium is reached, or they tend to diverge and destroy the structure.

We shall define Aeroelasticity as a phenomena involving interactions among Aerodynamic, Elastic and Inertial forces.

Collar (Collar, A.R. “ The expanding domain of Aeroelasticity” , Jl. of the Aeronautical Society, Vol.L, PP 613-636, Aug. 1946) has ingeniously classified problems in Aeroelasticity by means of a triangle of forces. This is known as Collar Triangle of Aeroelastic forces.

fig: Collar’s triangle of forces. or The Aeroelastic triangle of forces.

A

E I

A - Aerodynamic forcesE – Elastic forces I – Inertia forces.

SSAL

SSAL

CD

R

DS

V

DSA-DSAZ

BF

DSA: Aeroelastic effect on dynamic stability.

SSA: Aeroelastic effect on static stability

V: Mechanical vibrations

DS: Dynamic stability

F: FlutterB: BuffetingZ: Dynamic responseL: load distributionC: control effectivenessD: DivergenceR control system reversal

Referring to figure the three types of forces aerodynamic, elastic and inertia, represented by the symbols A, E and I are placed at the vertices of a triangle.

Each aeroelastic phenomenon can be located on the diagram according to its relation to the three vertices. Eg., Dynamic aeroelastic phenomena such as flutter, F, lie within the triangle, since they involve all three types of forces and must be bonded to all three vertices. Static aeroelastic phenomena such as wing divergence, D, lie outside the triangle on the upper left side, since they involve only aerodynamic and elastic forces.

Although it is difficult to define precise limits on the field of aeroelasticity, the classes of problems connected by solid lines to the vertices in the figure are usually taken as the principal ones.

Other border line fields also can be placed on the diagram. Eg., the field of mechanical vibration, V, and rigid body aerodynamic stability, DS, are connected to the vertices by dotted lines. It is very likely that in certain cases the dynamic stability problem is influenced by airplane flexibility and it would, therefore be moved in to the triangle , to correspond with DSA, where it would be regarded as a dynamic aeroelastic problem.

Definitions of Aeroelastic phenomenon: Flutter, F: A dynamic instability occurring in an aircraft in flight at a speed called flutter speed, where the elasticity of the structure plays an essential part in the instability.

Buffeting, B: Transient vibrations of aircraft structural components due to aerodynamic impulses produced by the wake behind wings , nacelle, fuselage pods, or other components of the airplane.

Dynamic response, Z: Transient response of aircraft structural components produced by suddenly applied loads due to gusts, landing, gun reactions, abrupt control motions, moving shock waves, or other dynamic loads.

Aeroelastic effects on stability, SA: Influence of the elastic deformations of the structure on dynamic and static airplane stability.

Load distribution, L:Influence of elastic deformations of the structure on the distribution of aerodynamic pressure over the structure.

Divergence, D: A static instability of a lifting surface of an aircraft in flight, at a speed called divergence speed, where the elasticity of the lifting surface plays an essential role in the instability.

Control effectiveness, C: Influence of the elastic deformations of the structure on the controllability of an airplane.

Control system reversal, R: A condition occurring in flight, at a speed called control reversal speed, at which the intended effects of displacing a given component of the control system are completely nullified by elastic deformations of the structure.

Aeroelastic effects:

1. Loss and reversal of Aileron control:- 2 D case.

Ailerons control the rolling motion of an airplane. When an aileron is displaced downward, the lift over the wing increases, thus producing a rolling moment. But the aileron deflection also creates a nose down aerodynamic pitching moment, which twists the wing in a direction tending to reduce the lift and hence reducing the rolling moment. As the elastic stiffness of the wing is independent of the flight speed, where as the aerodynamic force varies with U2, There exists a critical speed at which the aileron becomes completely ineffective.

When the air speed is higher than the critical reversal speed, the aileron control is reversed. The elastic efficiency of the aileron or simply the aileron efficiency can be defined as the ratio of the rolling moment produced by an aileron deflection to that produced by the same deflection on a hypothetical rigid wing of the same plan form.

2. Divergence of a Lifting surface:

The central problem in steady-state aeroelasticity is the effect of elastic deformation on the lift distribution over lifting surfaces such as airplane wings and tails. At lower speeds of flight , the effect of elastic deformation is small. But at higher speeds of flight, the effect of deformation may become so serious as to cause a wing to be unsuitable, or to render a control surface ineffective or even to reverse the sense of control.

For modern aircraft, the critical speeds of flight at which divergence sets in are higher than those of flutter or other aeroelastic instabilities. Hence the divergence speed itself is often of minor importance.

However, it is a convenient reference quantity for other aeroelastic phenomena; it enters in to the expressions for the effect of elastic deformation on lift distribution, static and dynamic stability of the airplane etc.

Wing divergence is a simple example of steady – state aeroelastic instability. If a wing in a steady flight is accidentally deformed, an aerodynamic moment will generally be induced which tends to twist the wing. This twisting is resisted by elastic moment. However since the elastic stiffness is independent of the speed of flight, where as the aerodynamic moment is proportional to the square of the flight speed, there may exist a critical speed, at which the elastic stiffness is barely sufficient to hold the wing in the disturbed position. Above such a critical speed, an infinitesimal accidental deformation of the wing will lead to large angle of twist. This critical is called the divergence speed, and the wing is then said to be torsionally divergent.

Coupling: When the forces produced by one motion excite the other, the two types of motions are then said to be coupled. Various forms of coupling occur: inertial, aerodynamic and elastic.

Aerodynamic coupling is associated with changes of lift produced by wing rotation or translation. A change of wing incidence produces a change of lift which causes translation, while a translation velocity results in an effective change in incidence, thereby yielding a lift which causes rotation. These aerodynamic forces, which oscillate in a flutter condition, act through a centre analogous to the aerodynamic centre of a wing in steady motion; this centre is known as the centre of independence.

Dynamic Aeroelasticity studies the interactions among aerodynamic, elastic, and inertial forces. Examples of dynamic aeroelastic phenomena are:Flutter, Buffeting, dynamic or forced response etc..

Flutter is a self-feeding and potentially destructive vibration where aerodynamic forces on an object coupled with a structure's natural mode of vibration to produce rapid periodic motion. Flutter can occur in any object within a strong fluid flow, under the conditions that a positive feedback occurs between the structure's natural vibration and the aerodynamic forces. That is, the vibrational movement of the object increases an aerodynamic load, which in turn drives the object to move further.

If the energy input by the aerodynamic excitation in a cycle is larger than that dissipated by the damping in the system, the amplitude of vibration will increase, resulting in self-exciting oscillation. The amplitude can thus build up and is only limited when the energy dissipated by aerodynamic and mechanical damping matches the energy input, which can result in large amplitude vibration and potentially lead to rapid failure.

Dynamic responseDynamic response or forced response is the response of an object to changes

in a fluid flow such as aircraft to gusts and other external atmospheric disturbances. Forced response is a concern in axial compressor and gas

turbine design, where one set of aerofoils pass through the wakes of the aerofoils upstream.

BuffetingBuffeting 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 down stream of the wing.

Further Reading Elements of Aeroelasticity

from Aircraft structures for engineering students

byTMG Megson.

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