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Flutter Excitation
One of the most dangerous events that can occur in flight is a phenomena called "flutter". Flutter is an aerodynamically induced vibration of a wing, tail, or control surface that can result in total structural failure in a matter of seconds. The prediction of flutter is not a precise science and requires flight verification that flutter will not occur within the normal flight envelope.
The aerodynamic surfaces of an airplane are constructed so that they can carry the loads that are produced in flight. For example the wing must be capable of supporting the weight of the airplane as well as the additional lift produced during turning flight. The resulting wing structure can be viewed as a blade or spring extending from the fuselage. If we "tap" the spring with a hammer, it will vibrate at a frequency which relates to the stiffness of the spring. A stiff spring will vibrate at a higher frequency than a more limber spring. This frequency is known as the "natural frequency" of the spring.
Flutter will usually occur at or near the natural frequency of the structure, that is, some small aerodynamic force will cause the structure to vibrate at its natural frequency. If this small force persists at the same frequency as the natural frequency of the structure, a condition called "resonance" occurs. Under a resonant condition, the amplitude of the vibration will increase dramatically in a very short time and can cause catastrophic failure in the structure.
The aerodynamic forces which can induce flutter are related to the dynamic pressure, or airspeed, of the airplane. If flutter-inducing forces are present they will increase as the airspeed is increased. Flutter characteristics can be explored by "tapping" the surface at progressively faster airspeeds, then watching how fast the vibrations decay or damp out. The vibrations will take longer to decay as the airspeed approaches a possible resonant condition. In this way potential flutter can be approached safely without actually reaching the resonant condition and experiencing sustained flutter.
The method for "tapping" the surface varies. On some airplanes a sharp control pulse is sufficient to excite the natural frequency of the surface. In most cases a special flutter excitation device is installed. This device will use either an aerodynamic vane or an unbalanced mass which is driven back and forth at the known natural frequency of the surface. The device is abruptly turned off and the natural damping characteristics of the vibrating surface are revealed. The analysis is similar to the frequency and damping analysis discussed under the "control pulse" maneuver, except that the structural (or flutter) frequencies are much higher.
Todo cuerpo, por mas complejo que sea tiene lo que se llama una frecuencia natural con la que vibra. La frecuencia natural de un cuerpo depende de las caracteristicas geometricas y del material del cuerpo, principalmente del momento de inercia, es decir de la masa y la forma en que esta se distribuye alrededor del centro de gravedad del cuerpo. Esta frecuencia basicamente determina a que frecuencia vibrará el cuerpo al recibir algun impacto o cualquier otro estimulo que lo haga vibrar. Como ejemplo, si agarras una barra de acero y la empotras en un extremo y calculas su frecuencia natural, al golpearla en el otro vibrara con esa frecuencia.Como afecta esto?? Si a esa misma barra le aplicaras una vibracion de frecuencia que coincida con la frecuencia natural de la barra, estas empezaran a vibrar en conjunto, y la amplitud de la vibracion crecera de forma indefinida. Esto se da ya que cada vez que la barra este oscilando en una direccion la vibracion tendra la misma direccion haciendo crecer la fuerza con que se mueve. Este fenomeno se conoce como resonancia, y hace que justamente, cuando la amplitud crece de forma ilimitada, los materiales se rompan.Esto es lo que paso en el puente de Tacoma si no me equivoco, pero no es el unico caso, la resonancia es un problema comun y muy severo. Si el puente empieza a oscilar en resonancia ira hacia arriba y hacia abajo cada vez apartandose mas de su linea media hasta que se rompa.
La frecuencia natural es la frecuencia a la que un sistema mecánico seguirá vibrando, después que se quita la señal de excitación. A veces se le llama la frecuencia de resonancia pero eso no es correcto ya que la frecuencia de resonancia es la frecuencia a la que vibraría el sistema si no hubiera amortiguación.De cualquier estructura física se puede hacer un modelo en forma de un número de resortes, masas y amortiguadores. Los amortiguadores absorben la energía pero los resortes y las masas no lo hacen. Como lo vimos en la sección anterior, un resorte y una masa interactúan uno con otro, de manera que forman un sistema que hace resonancia a su frecuencia natural característica. Si se le aplica energía a un sistema resorte-masa, el sistema vibrará a su frecuencia natural, y el nivel de las vibraciones dependerá de la fuerza de la fuente de energía y de la absorción inherente al sistema. . La frecuencia natural de un sistema resorte-masa no amortiguado se da en la siguiente ecuación:
Fn=(1/2pi) (raiz(k/m))
Donde Fn = la frecuencia naturalk = la constante del resorte, o rigidezm = la masaDe eso se puede ver que si la rigidez aumenta, la frecuencia natural también aumentará, y si la masa aumenta, la frecuencia natural disminuye. Si el sistema tiene absorción, lo que tienen todos los sistemas físicos, su frecuencia natural es un poco más baja y depende de la cantidad de absorción. Un gran número de sistemas resorte-masa-amortiguación que forman un sistema mecánico se llaman "grados de libertad", y la energía de vibración que se pone en la máquina, se distribuirá entre los grados de libertad en cantidades que dependerán de sus frecuencias naturales y de la amortiguación, así como de la frecuencia de la fuente de energía. Por esta razón, la vibración no se va a distribuir de manera uniforme en la máquina. Por ejemplo, en una máquina activada por un motor eléctrico una fuente mayor de energía de vibración es el desbalanceo residual del rotor del motor. Esto resultará en una vibración medible en los rodamientos del motor. Pero si la máquina tiene un grado de libertad con una frecuencia natural cerca de las RPM del rotor, su nivel de vibraciones puede ser muy alto, aunque puede estar ubicado a una gran distancia del motor. Es importante tener este hecho en mente, cuando se hace la evaluación de la vibración de una máquina. --la ubicación del nivel de vibración máximo no puede estar cerca de la fuente de energía de vibración. La energía de vibración
frecuentemente se mueve por largas distancias por tuberías, y puede ser destructiva, cuando encuentra una estructura remota con una frecuencia natural cerca de la de su fuente.
Abstract: A flutter exciter induces vibration either for actual aircraft flight testing or for wind tunnel model testing. The basic flutter exciter unit is a pair of rotatable concentric cylinders mounted on either a fixed vane or an aircraft wing or a tail surface. Each cylinder has a slot which allows the air flow to pass there through. By rotating the cylinders together, oscillating air pressures are induced on the fixed vane or the aircraft surface to which the cylinders are attached. The cylinders may be mounted at a trailing edge of either the fixed vane or the aircraft wing, to any tail surface, or on any other lifting surfaces of the aircraft itself. Thus, because the flutter exciter can be made as a completely self-contained unit, it may be simply mounted to any suitable hard point on either the test model or the aircraft. The power required to rotate the slotted cylinders is minimal, thus allowing the use of a low wattage motor.
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates generally to aerodynamic wing study and specifically to a device for inducing flutter in an aircraft wing during structural dynamic testing thereof.
2. Description of the Related Art
Flight flutter and structural dynamic testing of aircraft generally requires a method of exciting the structure beyond the use of free stream turbulence or "stick raps" by the pilot. Aircraft control surfaces can provide such excitation if the flight control actuator has sufficient output over the frequency range of interest. Since flight control actuators are usually not designed for high frequency operation, some form of external exciter system is typically used. The two primary types of exciters are inertial and aerodynamic.
Inertial exciters are unbalanced masses driven by either an hydraulic or an electric motor. The primary disadvantages of inertial exciters are their large size and their heavy weight. Correspondingly, large motors are required to drive thelarge masses of such inertial exciters.
Aerodynamic exciters are external lifting surfaces which are pitch-oscillated to obtain the required excitation forces. Aerodynamic vanes on small surfaces of the wing are quite efficient in generating the dynamic forces required for flight flutter tests. Typically, they require hydraulic actuation because of the relatively large power required to overcome aerodynamic and inertial loads. This requirement for hydraulic power adds a considerable complication to the installation of such a system. Quite often, the cost becomes prohibitive.
U.S. Pat. No. 3,552,192 was issued to Grosser on Jan. 5, 1971, for a rotary excitation device. In the flutter exciter system of Grosser, a rotating aerodynamic vane is mounted adjacent to the surface of the outer tip of an aircraft wing or horizontal stabilizer at right angles to the direction of flight. Grosser's excitation device comprises a vane which rotates at a constant rate about its mid-chord axis. Because the chordwise center of pressure of the rotating vane changes with the angular position of the vane during each rotation cycle, the torque and consequently the power required to drive the system can become a major deterrent in implementing the concept of Grosser's flutter exciter system.
Therefore, it remains a problem in the prior art technology to provide a flutter exciter system which imposes minimal power demands on existing hydraulic or electrical systems of the aircraft. Also. it remains a problem to make a completely self-contained flutter exciter unit which may be simply mounted to any suitable hard point on the aircraft.
SUMMARY AND OBJECTS OF THE INVENTION
The present invention may be summarized as a relatively simple aerodynamic flutter exciter electrically driven with very small power requirements. The performance characteristics of the flutter exciter comprising the present invention, as measured in a low speed wind tunnel, indicate that, although the force-producing capability of the flutter exciter is equivalent to the capability of a comparably sized flutter exciter of the oscillating vane-type, the power requirements of the present invention are very much smaller than the power requirements of such oscillating vane-type flutter exciter. Thus, this low input power demand makes feasible the use of a small electric motor which can be powered either by the direct current electrical system on board the aircraft or by a rechargeable battery pack.
Thus, the primary object of the present invention is to provide a self-contained flutter exciter unit which can be mounted at any suitable hard point on the aircraft with minimal installation difficulty and cost.
It is another object of the present invention to provide a flutter exciter system to replace current flight testing procedures which involve the use of atmospheric turbulence as a means of excitation so that dependence on the whims of nature, which often cause costly schedule delays, can be avoided.
It is a further object of the present invention to provide a strap-on structural flutter excitation system installed to be used repeatedly for testing a wide variety of research aircrafts.
It is another object of the present invention to provide a device for inducing flutter during the structural dynamic testing of an aircraft model in a wind tunnel.
A key advantage offered by the present invention over the known prior art technology is that the low input power required produces a relatively high level of dynamic excitation force.
This advantage and other features of the present invention will become more readily apparent from the following brief description of the drawings and the accompanying detailed description of the preferred embodiments.
BRIEF DESCRIPTION OFTHE DRAWINGS
FIG. 1 is a perspective view of the flutter exciter of a first embodiment of the present invention with a rotating slotted cylinder along the trailing edge of a fixed vane.
FIG. 2 is a top plan view of the flutter exciter of the first embodiment with parts broken away to show the rotary flap drive unit and the slot opening mechanisms.
FIG. 3 is a cross-sectional view of the flutter exciter of the first embodiment taken along line 3--3 in FIG. 2.
FIG. 4A is a perspective view of the flutter exciter of a second embodiment of the present invention with a rotating slotted cylinder mounted along the trailing edge of the aircraft.
FIG. 4B is a perspective view of the flutter exciter of a third embodiment of the present invention with a rotating slotted cylinder mounted on a surface of a wing or a tail of the aircraft.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 1 depicts the primary components of the flutter exciter system which may be mounted either on a model being tested in a wind tunnel or on an actual aircraft being tested in the atmosphere. A base plate 10 carries a pod 12 on which a fixed vane 14 is mounted in a cantilevered manner to a wing tip or an empennage of either a wind tunnel model or a full-scale aircraft.
As shown in FIG. 2, the basic flutter exciter unit includes a rotating slotted outer cylinder 16 and a rotating slotted inner cylinder 20 both located at a trailing edge of the fixed vane 14. Two span wise slots 18, symmetrically aligned on opposite quadrants of the cylinders 16 and 20, provide for the passage of air flow through the slots 18 such that, when the cylinders 16 and 20 rotate together, the air flow is directed upwardly and downwardly twice during each rotational cycle. Since the cylinders 16 and 20 rotate together at a uniform or slowly varying speed, the inertia loads normally associated with an oscillating trailing edge control surface are not present. Furthermore, the aerodynamic hinge moments due to control surface deflection are essentially zero for the rotating flap because the aerodynamic forces acting on opposite sectors of the cylinders 16 and 20 tend to cancel each other. Thus, the two primary sources of power consumption found in conventional oscillating vane systems, i.e. inertia and aerodynamic hinge moments, are virtually eliminated in the flutter exciter of the present invention.
FIG. 2 further illustrates a mechanism for remotely changing the open area in the span wise slots 18. The area is open in the slots 18 for the passage of the air flow there through and, consequently, the dynamic excitation force is determined by the angular relation between the two concentric slotted cylinders 16 and 20.
As shown in FIG. 3, the inner cylinder 20 may be rotated independently of the outer cylinder 16 so that the slot 18 at the trailing edge of the fixed vane 14 is fully opened when an angle .theta. between the edges of the outer cylinder 16 and the inner cylinder 20 is zero and is fully closed when the angle .theta. is 90.degree.. In other words, the inner cylinder 20 is rotated independently only when it is desired to change the size of the opening in the slot 18 in order to adjust the amplitude of the vibration caused by the flutter exciter.
Returning to FIG. 2, the outer cylinder 16 is driven through bevel gears 22 by a variable speed direct current motor 24. The inner cylinder 20 is connected to and rotates with the outer cylinder 16 via a splined shaft 26. This shaft 26 isdriven by the outer cylinder 16 through a pin 28 that projects from the splined shaft 26 through a slot 30 in a collar 32 attached to the right hand end of the outer cylinder 16. Thus, in the manner of a so-called "Yankee screwdriver", if the splined shaft 26 is moved axially, the shaft 26 also rotates relative to the collar 32 through an angle .theta. which is determined by the pitch of the slot 30 which, although shown straight in FIG. 2, actually spirals helically around the cylindrial portion ofthe collar 32. Since the inner cylinder 20 is connected to the splined shaft 26, such inner cylinder 20 also rotates continuously with the outer cylinder 16 at the same angle .theta. relative to the outer cylinder 16. The axial position of the splined shaft 26 can be shifted by a rack 34 and a pinion gear 36 actuated by a second motor (not shown).
In addition to the control of the dynamic force amplitude, by the use of a conventional electronic phase-control circuit (not shown) connected to the first motor 24 and the second motor (not shown), two or more flutter exciter units of the present invention can be driven either in phase or 180.degree. out of phase with each other so as to emphasize symmetric or anti symmetric vibration modes.
FIGS. 4A and 4B show two alternative embodiments of the flutter exciter of the present invention. A lifting surface 44, such as a wing or an empennage of an aircraft or a wind tunnel model, has either one of two rotating cylinders 46 with an open span wise slot 48 mounted at a selected location on the lifting surface 44, e.g., along the trailing edge in FIG. 4A and on the upper surface in FIG. 4B. Each rotating outer cylinder 46 contains a rotating inner cylinder 20 shown in FIG. 2. For the two examples of the trailing edge and the upper surface shown in FIGS. 4A and 4B, the dynamic excitation force is induced by pressure changes across the lifting surface 44 itself rather than across the separate fixed vane 14 which would be mounted at a tip of the lifting surface 44 or the empennage by the base plate 10 shown in FIGS. 1-3. However, the embodiment shown in FIG. 4B may also be mounted on an undersurface of the wing, on either an upper or a lower surface of a horizontal tail fin, or on aside surface of a
vertical tail section.
The operation of the flutter exciter of the present invention may be simply described as follows. The excitation frequency can be varied by electrically controlling the rotational speed of the first motor 24 shown in FIG. 2. Referring to FIG.3, the amplitude of excitation force can be controlled either remotely by electrical devices (not shown) wired to the second motor (not shown) or mechanically preset by varying the opening of the slot 18 in the outer cylinder 16 by independently rotating the inner cylinder 20 to a selected angle .theta.. On a model aircraft structure on which any of the three embodiments shown in FIGS. 1, 4A and 4B are used for testing in a wind tunnel, the air flow passes through the slots 18 or 48 in the cylinders 16or 46 and is redirected in order to induce flutter in the model aircraft structure. Measurements are then taken by various conventional instruments (not shown) of the amount of vibration or flutter induced in the aircraft structure.
On an actual aircraft in which any of the three embodiments shown in FIGS. 1, 4A and 4B are used for testing purposes in the atmosphere, the plane must first achieve flight suitable for testing. For example, a pilot may seek level stable flight and then either the pilot or a technician remotely controls the operation of the flutter exciter by adjusting the rotational speed of the first motor 24 to control the frequency of rotation of the two concentric cylinders 16 and 20 and by adjusting the size of the opening in the slot 18 or 48 to control the amplitude of the excitation force. Measurements of the amount of dynamic response excited in the wing 44 or empennage are subsequently recorded by conventional instrumentation packages (not shown)on board the aircraft.
The aerodynamic performance and power requirements of the flutter exciter of the present invention have been demonstrated on a two-dimensional model of a fixed vane 14 in a wind tunnel at low speeds and at low Reynolds numbers to be more satisfactory than known prior art devices for exciting flutter. In one example, the maximum change in lift with the changing position of the cylinder 16 occurred when the vane chord was approximately four times the diameter of the rotary cylinder 16. The maximum lift coefficient variation for the condition was .+-.0.35. Thus, at an airspeed of about 500 miles per hour, this lift coefficient would produce a dynamic lift force of nearly .+-.300 pounds per square foot of area (vane plus flap).
The foregoing preferred embodiments are considered illustrative only. Numerous other modifications will readily occur to those persons skilled in aeronautical technology after reading the foregoing specification. Consequently, the exact construction and operation shown and described above is not limited thereto but rather is defined by the following claims.
* * * * *
A380 MSN001 was equipped with more than100 measurement points uniformly distributed all over the primary aircraft structure.
Aeroelasticity, the interaction between inertial, elastic, and aerodynamic forces, plays a vital role in aircraft design. And as soon as you add four enormous engines and a significant increase in size and flexibility, it is not surprising that aeroelastic behavior evolves, becoming more and more complex.
Along with the aircraft characteristics, modal identification methods used during flutter testing have evolved to ensure correct parameter identification. Frequencies and damping value estimations have to be as accurate as possible to define the aircraft fluttering margins used during those first mission-critical in-flight test campaigns.
Flutter testing can be broken into three segments: real time, near real time, and offline. In-flight real-time test campaigns acquire live data during the test flight mostly as a safety check to continue the flight envelope. Near real-time testing focuses on rapid modal estimation to determine the overall safety of the flight and the flutter test program. Offline deals with the finer analysis of the recorded flight data and final report production.
The Airbus flutter team in Toulouse, France, faced challenges working on the Airbus A380 campaign, but there were issues it had faced before with the Airbus A340 flutter campaign: high modal density and similar mode shapes, both placed in a low narrow frequency band.
In terms of modal identification, these new precise requirements called for a better-defined and better-equipped testing installation. This meant digging a bit to find the right kind of process. Measured data needed to be recorded at enough locations with high enough quality to improve power spectra and transfer function estimates and avoid spatial aliasing when working out aircraft deformed shapes. This required some innovative thinking and process validation in regard to current techniques.
Since 2001, Airbus France and LMS International have been cooperating in regard to several EUREKA projects called “FLITE” (Flight Test Easy). An intergovernmental initiative to support market-oriented European R&D, the EUREKA FLITE projects focus on bringing new and powerful tools to structural engineers and aircraft designers, improving the quality and usefulness of data gathered during flight testing.
In late 2007, LMS and Airbus agreed to start a project to evaluate LMS PolyMAX, an integrated part of the LMS Test.Lab Structures suite as a key solution to achieve high-quality offline in-flight data processing for flutter testing.
In the past, the Flight Test Departments of Airbus France performed data analysis using its in-house near real-time analysis package and transferred the results together with the raw data to Airbus Germany where the numerical flutter predictions were correlated with actual flight tests. However, Airbus France felt the need to carry out some more in-depth data processing, so that it could transfer more complete results to Germany.
“Clearly, we needed a solution that would improve the alignment between online in-flight analysis occurring in Toulouse and the post-processing completed in the design center in Airbus Germany. At this stage, we are very pleased with the results. LMS Test.Lab is able to provide us with the right type of results,” said Jean Roubertier, flight test department aeroelasticity expert at Airbus.
Considering that the 525-seat Airbus A380 is the largest commercial passenger aircraft in the skies today, it is not surprising that simply due to its sheer size, the acquired in-flight testing data is record-breaking as well.
“With more than 100 sensors, this was one of the largest setups for an in-flight flutter test campaign I have ever seen. Also the amount of tests under different flight conditions is impressive. The resulting database is immense, and efficient processing and report generation capabilities are required,” said Bart Peeters, LMS Research Project Manager.
The Airbus Flutter team in Toulouse performed a variety of excitations including control surfaces sine sweeps and pulses. Pulses are currently used to ensure crew and aircraft safety, whereas sweeps are used to work out more accurate results allowing to update theoretical FE models. By integrating pulses into the process, flutter flights duration time has been considerably reduced.
The basic concept behind the project was to compare classical experimental modal analysis (EMA) with LMS Test.Lab’s Operational Modal Analysis (OMA) technique. In classical EMA, the control surface excitation and aircraft response signals are converted to Frequency Response Functions (FRFs). During the actual flight, other excitation sources, such as turbulence are present. Sometimes, this results in noisy FRFs. For example, an aircraft tail response sensor receives a rather limited contribution from the wing excitation. Therefore, the idea arose to neglect the excitation signal and apply OMA to the aircraft acceleration signals.
“We actually achieved better results using OMA than with classical EMA. We found more modes. The synthesis was better with higher correlation and fewer errors. And the in-flight mode shapes looked much nicer,” said Miquel Angel Oliver Escandell. “This was thanks to the amount of sensors we used and the OMA capabilities of LMS Test.Lab.”
During the comparison testing, the flutter team at Airbus used LMS PolyMAX during sweep excitations of the aircraft. Results, using an exponential window of 5% appear to be good, supplying high synthesis correlations (98% using just two references) and clear stabilization diagrams. “We’ve been extremely impressed by the flutter analysis results and the way that the LMS Test.Lab software can handle the challenges of processing the immense amount of Airbus A380 in-flight data during the off-line analysis,” said Jean Roubertier.
Jennifer Schlegel, Senior Editor, LMS International, Leuven, Belgium, wrote this article for Aerospace Engineering & Manufacturing.
Aerodynamic Flutter
Flutter is a dangerous phenomenon encountered in flexible structures subjected to
aerodynamic forces. This includes aircraft, buildings, telegraph wires, stop signs, and
bridges. Flutter occurs as a result of interactions between aerodynamics, stiffness, and
inertial forces on a structure. In an aircraft, as the speed of the wind increases, there may
be a point at which the structural damping is insufficient to damp out the motions which
are increasing due to aerodynamic energy being added to the structure. This vibration
can cause structural failure and therefore considering flutter characteristics is an essential
part of designing an aircraft.
Flutter Motion
The basic type of flutter of aircraft wing is described here. Flutter may be initiated by a
rotation of the airfoil (see t=0 in Figure 1). As the increased force causes the airfoil to
rise, the torsional stiffness of the structure returns the airfoil to zero rotation (t=T/4 in
Figure 1). The bending stiffness of the structure tries to return the airfoil to the neutral
position, but now the airfoil rotates in a nose-down position (t=T/2 in Figure 1). Again
the increased force causes the airfoil to plunge and the torsional stiffness returns the
airfoil to zero rotation (t=3T/4). The cycle is completed when the airfoil returns to the
neutral position with a nose-up rotation. Notice that the maximum rotation leads the
maximum rise or plunge by 90 degrees (T/4). As time increases, the plunge motion tends
to damp out, but the rotation motion diverges. If the motion is allowed to continue, the
forces due to the rotation will cause the structure to fail. [Click here to see a wind tunnel
test model exhibiting flutter.]
Figure 1 Rotation and Plunge Motion for an Airfoil Exhibiting Flutter This flutter is caused by the coalescence of two structural modes – pitch and plunge (or
wing-bending) motion. This example wing has two basic degrees of freedom or natural
modes of vibration: pitch and plunge (bending). The pitch mode is rotational and the
bending mode is a vertical up and down motion at the wing tip. As the airfoil flies at
increasing speed, the frequencies of these modes coalesce or come together to create one
mode at the flutter frequency and flutter condition. This is the flutter resonance.
Types of Flutter
Airfoils are used in many places on an airplane. The most obvious is the wing, but airfoil
shapes are also used in the tail, propellers and control surfaces such as ailerons, rudders
and stabilizers as shown in Figure 2. All of these conditions must be analyzed and tested
to insure that flutter does not occur.
Figure 2 Airfoil Sections on a Typical Aircraft
(http://www.wingsoverkansas.com/learn/article.asp?id=256)
There is other flutter behavior that must be considered when designing aircraft: panel
flutter, galloping flutter, stall flutter, limit cycle oscillations (LCO) or buzz, and propeller
or engine whirl flutter. There can also be flutter due to stores mounted on the wing.
Panel flutter can occur when a surface is not adequately supported (think of the skin of an
airplane acting like a drumhead). Figure 3 illustrates panel flutter motion.
Figure 3 Panel Flutter
(http://www.va.afrl.af.mil/coe/comp/research/MDC/mdc_images/panel.jpg) Galloping flutter, or wake vortex flutter, was the cause of failure of the Tacoma Narrows
Bridge. [Click here to view video.] This phenomenon can be observed frequently along
the roadside when telephone and power lines “gallop” due to strong winds. You may
also observe car radio antenna aerials whipping under certain driving speeds. The cause
of the galloping motion is formation of wake vortices downstream of the object. As
shown in Figure 4, the vortices are shed alternately from one side of the object and then
the other. These cause oscillatory forces and produce the back-and-forth motion. This
type of flutter is an important design consideration for launch vehicles exposed to ground
winds. [If you want to experiment with wake vortex shedding, click here.]
Figure 4 Wake Vortex Shedding from a Cylinder
Stall flutter is a torsional mode of flutter that occurs on wings at high loading conditions
near the stall speed. Because the airflow separates during stall, this single degree-offreedom flutter cannot be explained by classical flutter theory.
Limit cycle oscillation (LCO) behavior is characterized by constant amplitude, periodic
structural response at frequencies that are those of the aeroelastically-loaded structure.
LCO is typically limited to a narrow region in Mach number or angle-of-attack signaling
the onset of flow separation.
Engine whirl flutter is a precession-type instability that can occur on a flexibly mounted
engine-propeller combination. The phenomenon involves a complex interaction of
engine mount stiffness, gyroscopic torques of the engine and propeller combination, and
the natural flutter frequency of the wing structure. [Click here to see a model exhibiting
whirl flutter.]Figure 5 Engine Whirl Flutter
(http://www.acoustics.org/press/133rd/2psa1.html)
Classical Flutter Definition
As early aircraft were able to fly at greater speed, flutter may have caused many crashes.
The flutter phenomenon was first identified in 1918 on a Handley Page bomber in
Lanchester, England. The flutter mechanism consisted of a coupling of the fuselage
torsion mode with an anti-symmetric elevator rotation mode. The elevators on this
airplane were independently actuated. The solution to the problem was to interconnect
the elevators with a torque tube.
Scientists and engineers studied flutter and developed theories for the cause and
mathematical tools to analyze the behavior. In the 1920s and 1930s, unsteady
aerodynamic theory was developed. Closed-form solutions to simple, academic problems
were studied in the 1940s and 1950s. In the next thirty years, strip theory aerodynamics,
beam structural models, unsteady lifting surface methods (e.g. double-lattice) and finite
element models expanded analysis capabilities. The advent of digital computers has
further supported the development of other powerful methods. Disciplines involved in
analyzing flutter include aerodynamics, structural finite element modeling, control theory
(specifically aeroservoelasticity), and structural dynamics.
The following example of a simple two degree-of-freedom model is fundamental to
understanding flutter behavior. Aerodynamic forces excite the structural spring/mass
system (see Figure 9). The plunge spring represents the bending stiffness of the structure
and the rotation spring represents the torsional stiffness. The shape of the airfoil
determines the aerodynamic center. The center of gravity is determined by the mass
distribution of the cross-section (that is, how the airfoil is constructed). The model
represents two “modes” – plunge and rotation as shown in Figure 6. Figure 7 shows a
similar model for an airfoil with a control surface. The aerodynamic forces are illustrated
in Figures 8 and 9. Figure 6 Airfoil Flutter Model and Modes
Figure 7 Wing/Aileron Flutter Model and Modes Figure 8 Phasing of Aerodynamic Forces
Figure 9 Aerodynamic Lag Flutter Equation of Motion (for the more advanced student)
If modes of structural vibration are used in a dynamic analysis, the below equation can be
used to determine a model’s flutter characteristics. This equation is the result of
assuming simple harmonic motion { } { }
i t
h
u t u e
ω
( ) = and placing this into the
corresponding second order ordinary differential equations that describe the linear
dynamic behavior of a structure that is subjected to forces and moments due to fluid flow.
Figure 10 shows a flow diagram with the operations to solve the below equation.
{ } 0
4 2
2
2
=
⎥⎦⎤⎢⎣⎡⎟⎠⎞⎜⎝⎛⎟ + −
⎠⎞⎜⎝⎛+ − h
R
hh
hh
I
hh
hh hh
u
V Q
p K
k
cVQ
M p B
ρ ρ
Mhh – modal mass matrix
Bhh – modal damping matrix
Khh – modal stiffness matrix
Q
I
hh – generalized aerodynamic damping matrix
Q
R
hh – generalized aerodynamic stiffness matrix
ρ – air density
c – mean aerodynamic chord length
V – airspeed
k = ωc/2V – reduced frequency
ω−circular frequency
p- iω − (i= −1 )
uh – modal displacements
Figure 10 Flow Diagram for Solution of Flutter Equations of Motion
(at a Single Mach Number) One common form of flutter analysis is the V-g analysis. In V-g analysis, the structural
damping of all the modes of vibration is assumed to have one unknown value, g. In
Figure 11, the results for two modes (roots of the flutter determinant) of the simple wing
model with 2 degrees of freedom are shown in the form of frequency versus velocity and
damping versus velocity curves. In the bottom plot of Figure 11, the velocity at which
the upper curve passes through g=0 corresponds to the flutter velocity of the model if the
(conservative) assumption of zero structural damping is made. One is then able to
determine the flutter frequency of the model using the upper plot of Figure 11 and
picking off the frequency value of the unstable mode at the flutter velocity value. The
slope of the damping versus velocity curve as it passes through the flutter velocity can be
thought of as a qualitative measure of how violently the oscillations would occur during
accelerated flight.
Figure 11 Velocity-Frequency and Velocity-Damping Curves Flutter Fixes
Because flutter can be analyzed, designs can be modified to prevent flutter before an
aircraft is built, tested and flown. One design parameter is the maximum air speed. In
particular, the ratio of the energy input to the energy dissipated will depend on the air
speed. A steady oscillation may occur when this ratio is unity. The air speed for this
case is called the "critical air speed." An aircraft may have various possible flutter
modes. Ideally, the lowest critical speed exceeds the highest possible flying speed by a
reasonable safety margin.
There are several additional measures to prevent flutter. One method is to uncouple the
torsion and bending motion by modifying the mass distribution to move the center of
gravity closer to the center of twist (see Figure 12 for some examples). Another method
is to increase the stiffness/mass ratios within the structure. This would increase the
natural frequencies. Note that the energy input per cycle during flutter is nearly
independent of frequency. The energy dissipated per cycle is proportional to frequency,
however.
Figure 12 Potential Modifications to Mass Balance of Aileron
Flutter characteristics of a model are a function of many structural parameters including
the shape of the airfoil section, the elastic axis position, the position of the center of
gravity, the airfoil section mass and mass moment of inertia about the elastic axis, the
torsion rigidity and the frequency separation between the plunge and rotation mode.
The two plots in Figure 13 show how varying two of these parameters, rotational stiffness
and elastic axis, affects the flutter and divergence characteristics of a two-dimensional
flutter model. In the top plot of this figure, for a given rotational stiffness, the flutterspeed of the model is plotted versus the position of the elastic axis (point where springs
act through in Figure 6). In the bottom figure, the required rotational stiffness value so
that a particular form of instability will not occur is plotted versus elastic axis position.
Using this figure, one can determine for a given elastic axis position, what the rotational
stiffness must be such that flutter and static divergence do not occur.
Figure 13 Stiffness Requirements
Testing
After the design is analyzed the aircraft undergoes wind tunnel testing (Figure 14) and
flight-testing to verify the analysis. Low-speed wind tunnel testing of the full-span model
with scaled stiffness and mass properties visually identifies instabilities. [Click here to
see a video of a wind tunnel test.] High-speed wind tunnel tests investigate the transonic
flight regime. The models are heavily instrumented to verify aerodynamic forces and
reactions.
One facility used extensively for flutter clearance testing (which means to insure that
flutter does not occur within the envelope of where the aircraft will fly) is the NASA
Langley Research Center’s Transonic Dynamics Tunnel (TDT). The NASA Langley
TDT has provided a unique capability for aeroelastic testing for over forty years. [Click
here to learn more about flutter testing.]Flutter clearance or risk reduction tests are aimed at uncovering potential flutter problems
and identifying potential solutions of a specific design through airplane configuration
studies and tests of various components.
Wind-tunnel models are dynamically and aeroelastically scaled to a “theoretical” airplane
configuration. The results from these tests are considered experimental research that
contributes to the flutter clearance of the aircraft configuration.
Finally, flight-testing is performed at many conditions in the flight envelope. The control
surfaces are excited and response characteristics are measured. As speed is incrementally
increased, frequency and damping trends are calculated from the measured responses. A
successful design exhibits no flutter behavior in the flight envelope.
Figure 14 Wind Tunnel Test Model in the NASA Langley TDT
(http://lisar.larc.nasa.gov/UTILS/info.cgi?id=EL-1996-00023)
Contributed by
Chad Hebert, NextGen Aeronautics
Dave Cowan, NextGen Aeronautics
Attar Peter J, Contr AFRL/VAAC
Carol D. Weiseman, NASA Langley Research Center
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The tail control surfaces on F-14s are known as "rolling tails", in that the aircraft does not have ailerons on the wings to control roll. Roll control is instead provided at low speeds by wing-mounted spoilers and at high speeds by differential horizontal stabilizer deflection. This configuration also produces side force, or yaw, which contributed to the inadvertent spin entries. This large tail configuration is to aid in takeoff from aircraft carriers, by providing more pitch moment.
The paper studies the feasibility of applying piezoelectric actuators to suppress aeroelastic vibrations in a flexible aircraft so that the aeroelastic response can be tailored to comply with specified dynamic performance characteristics. To that end, an adaptive aeroelastic flight vehicle demonstrator concept was designed, developed, manufactured and tested. Closed-loop buffet attenuation, gust response alleviation and flutter suppression results are presented. The performance of the active aeroelastic control approach using piezoelectric actuators is compared to the performance of the aerodynamic control surfaces. Issues related to instrumentation for flight testing are presented as well.
