ST RU C T U RA L
DYNAMICS
Aeroelasticity and Flutter
..
Universidad Autnoma de Nuevo Len
Facultad de Ingeniera Mecnica y Elctrica
Introduction to aeroelasticity
Aeroelasticity is the science of the interaction of elastic, inertia and
aerodynamic forces on a structure
Forces due to air
acting on a body
Prediction of shape of
Inertial forces an elastic body under a
load
Aeroelastic phenomena
Static aeroelasticity
wing divergence , aero/structure stiffness
load redistribution - drag, stresses change
aileron reversal, lack of control
lift ineffectiveness, vertical tail yaw control
Dynamic aeroelasticity
Flutter and dynamic response
self-excited wing vibration/destruction
self-excited panel vibration
Static Aeroelasticity
Study of flight vehicle phenomena associated with interaction of
aerodynamic loading induced by steady flow and the resulting elastic
deformation of the lifting surface structure.
Static instabilities: Can result in catastrophic failure.
Aerodynamic
forces
Elastic
Forces Static
aeroelasticity
It is thought that Langley attempt to fly failed due to divergence
Static Aeroelasticity
Divergence
The lift force increase with the square of the speed and with the
angle of incidence.
Lift will cause the surface to twist, causing the angle to increase thus
increasing the aerodynamic force and so on until aequilibrium
condition is reached
Divergence occurs if torsional stiffness is not enough
Static Aeroelasticity
In modern aircraft, flutter speed is reached well before divergence
speed, i.e. divergency is not normally a problem.
However, it is considered as a part of the aircraft certification as it is
a measure of the general stiffness of the structure.
CS-25.629,FAR-25,
Static Aeroelasticity
Control Reversal
Another aeroelastic phenomenon is the fact that the effectiveness of atrailing
edge control surface decreases as speed increases.
This is because the upwards control force associated with a trailing-edge down
control deflection acts behind the elastic axis and causes the whole surface to
twist, leading-edge down. The effect of this twist is to reduce the effectiveness of
the control deflection in comparison with a rigid surface
Control effectiveness. (A) Rigid surface; (B) flexible surface.
Static Aeroelasticity
Control Reversal
Reduced ability, or loss of ability, to roll or turn quickly
The amount of airflow over the wing becomes so high that the force generated by the ailerons is
enough to twist the wing itself, due to insufficient torsional stiffness of the wing.When the aileron is
deflected upwards in order to make that wing move down, the wing twists in the opposite
direction.The net result is that the airflow is directed down instead of up and the wing moves
upward, opposite of what was expected.
Dynamic aeroelasticity, flutter
Flutter is adangerous phenomenon encountered in flexible structures
subjected to aerodynamic forces.Flutter occurs as a result of interactions
between aerodynamics, stiffness, and inertial forces on a structure.
Aircraft, buildings, transmission lines, stop signs, bridges etc.
Flutter Model
Flutter is an instability of the aircraft where, beyond the `flutter' speed,
vibration of the structure increases in amplitude, theoretically without limit.
Flutter can lead to the destruction of the aircraft in a very short time. It has
been a major problem historically and still is today.
The first known example of flutter was in 1916 when the Handley PageO/
400 bomber experienced violent tail oscillations. Since then, there have
been many flutter incidents, some with catastrophic consequences to
human life.
Flutter Model
Violent oscillations were observed in the fuselage and horizontal tail. It was
found that the fuselage and tail had two low frequency modes. In one mode, the
left and right elevators oscillated about their hinges 180 degrees out of phase.
Elevators were connected by a
weak spring.
Second mode, fuselage
oscillated in torsion.
Possible cause of the problem,
coupling between the two
modes.
Torsional stiffness connector
between elevators solved the
problem
Handley Page O/400
Flutter Motion
Flutter may be initiated by arotation of the airfoil. As the increased force
causes the airfoil to rise, the torsional stiffness of the structure returns the
airfoil to zero rotation.
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.
The increased force causes the airfoil to plunge and the torsional stiffness
returns the airfoil to zero rotation.
Flutter Motion
The cycle is completed when the airfoil returns to the neutral position with a
nose-up rotation.
If the motion is allowed to continue, the forces due to the rotation will cause
the structure to fail.
This flutter is caused by the coalescence of two structural modes (DOFs) pitch and plunge (or wing-
bending) motion.The pitch mode is rotational and the bending mode is avertical up and down motion
at the wing tip. As the airfoil flies at increasing speed, the frequencies of these modes coalesce to
create one mode at the flutter frequency and flutter condition.
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
stabilizers
rudders
propellers
elevators
aileron
Panel flutter, galloping flutter, stall flutter, propeller or engine whirl flutter.
Types of flutter
Panel flutter can occur when asurface is not adequately supported (think of the
skin of an airplane acting like a drumhead).
Galloping flutter, or wake vortex flutter, was the cause of failure of the Tacoma
Narrows Bridge.
Types of flutter
Stall flutter is atorsional mode of flutter that occurs on wings at high loading
conditions near the stall speed. (speed below which the airplane cannot create
enough lift to sustain its weight in 1g flight)
Engine whirl flutter is aprecession-type instability that can occur on aflexibly
mounted engine-propeller combination.The phenomenon involves acomplex
interaction of engine mount stiffness, gyroscopic torques of the engine and
propeller combination, and the natural flutter frequency of the wing structure.
Flutter Model
The basic mathematical model of the aircraft must be able to represent its
vibration behavior over the frequency range of interest, typically 040 Hz for a
large commercial aircraft, 060 Hz for asmall commercial aircraft and 080 Hz
for a military aircraft.
Simplified model
Aerodynamic forces excite the structural spring/mass system.
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.
The model represents two modes plunge and rotation
Simplified model
The model represents two modes plunge and rotation
Simplified model with control surface
The model represents two modes plunge and rotation
Flutter Motion
Classical Flutter
aileron frequency & motion wing bending and torsion
One degree of freedom flutter
Only rotational mode considered
Equation of motion given by: Aerodynamic moment depends upon:
Jp!! k M t
Freestream air density
Harmonic motion considered Mach number
t ei t Nature of flow (unsteadiness)
The aerodynamic pitching Lift force
moment is defined as:
M t Mei t
Two degrees of freedom flutter
Plunge and rotational mode considered
Equations of motion given by: Harmonic motion considered
m h!! x!! khh L t ht hei t
Jp!! mbx k M t t ei t
Where the static unbalance parameter is The aerodynamic pitching
x e a moment and lift defined as:
Positive when the center of mass is L t Lei t
towards the trailing edge from the
reference point M t Mei t
Multiple degree of freedom models
Stick beam or finite element models
Multiple degree of freedom models
Determine modes and perform modal decomposition
Introduce aerodynamic forces
Determine stability of system over arange of speeds, Mach numbers and
frequency parameters
Usually flutter calculation is presented as plots of frequency and damping
against speed for a particular Mach number or altitude
Flutter condition reached when
damping becomes zero.
Flutter speed is obtained for a
range of payload and fuel states.
Flutter speed can be increased by
design changes, typically must not
be less than 1.15 times the
nominal speed
Flutter fixes
Uncouple torsion and bending modes modifying mass distributionto move the
center of gravity closer to the center of twist.
Increase stiffness and mass ratios within the structure, i.e. torsional stiffness to
uncouple modes.
Increase stiffness in control surfaces.
Usually these methods increase weight and stiffness thus reducing fuel efficiency.
Flutter active control is also available through control surfaces.
Validation by test
Aircraft, very complex structure.
Stiffness at the major structural joints (e.g., wing/fuselage and wing/engine) may
be incorrectly modeled.
This may lead to errors in the modes and therefore in the flutter predictions.
Ground Vibration Test (GVT). Find natural frequencies, mode shapes, modal mass
stiffness and damping, very similar to modal testing.
Validation by test
Aircraft suspended on elastic supports (elastic cords, pneumatic air springs,
deflated tyres, etc).
Several shakers used (2 to 6) and instrumented with alatge number odf
accelerometers (200 to 1000)
Different excitation methods used to calculate modes and update the
mathematical models
Other aeroelastic phenomena
Flight loads; manoeuvres.
Gusts: Vertical, lateral, or longitudinal.
Buffet and buffeting: Caused by separated flow. i.e. turbulence.
Acoustic excitation. Jet flux cause panels to vibrate.
Gunfire loads and store release.
Birdstrike.
References
Encyclopaedia of vibration, Edited by: Braun, Simon G.; Ewins, David J.; Rao,
Singiresu S. 2002 Elsevier
Introduction of structural dynamics and aeroelasticity, Hodges and Pierce,
Cambridge aerospace series, 2008.
Inside Structural Dynamics, AIAA,http://www.cs.wright.edu/~jslater/
SDTCOutreachWebsite/sitemap.htm
