STRUCTURAL DYNAMICS Ae A er oe oela las st ici icity ty and Flutter …... ….
Universidad Universi dad Autónoma de Nue Nuevo vo León L eón Facul acultad tad de de Ingenie Ingeniería ría Mec Mecán ánic ica a y Eléctrica
Introduction t o aeroelas aeroelasticit ticity y Aero Ae roel elas asti tici city ty is th the e science of th the e int inter erac acti tion on of elastic, in iner erti tia a and aerody aer odynam namic ic forces on a st stru ruct ctur ure e Forces due to air acting on a body
Inertial Inerti al fo forc rces es
Prediction of shape of an el elas asti tic c body body und under er a load
Aeroelastic phenomena Static aeroe aeroelastici lasticity ty wing diverg divergenc ence e , aero/ aero/str struct ucture ure stif stiffne fness ss load redist redi stri ribu butition on - dra drag, g, st stre ress sses es chang nge e aileron ailer on reve revers rsal al,, lac lack k of con contr trol ol lilift ft ine ineff ffec ectiv tiven enes ess, s, vertical tail yaw yaw co cont ntro roll
Dynamic aeroelasticity Flutter and dynamic response self-excited wing vibration/destruction self-ex sel f-excite cited d pane panell 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.
Elastic Forces
Aerodynamic 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 a equilibrium 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.
• • • • Handley Page O/400
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
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 (DOF´s) pitch and plunge (or wingbending) 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
rudders
stabilizers 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 a precession-type instability that can occur on a flexibly 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 0 ±40 Hz for a large commercial aircraft, 0±60 Hz for asmall commercial aircraft and 0±80 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: !! J M t p k
Harmonic motion considered
t ei
t
The aerodynamic pitching moment is defined as: M t Mei t
Aerodynamic moment depends upon: •Freestream air density •Mach number •Nature of flow (unsteadiness) •Lift force
Two degrees of freedom flutter Plunge and rotational mode considered
Equations of motion given by:
m h!! x !! k hh L t !! J p mbx k M t
Where the static unbalance parameter is
x e a Positive when the center of mass is towards the trailing edge from the reference point
Harmonic motion considered ht hei t
t ei
t
The aerodynamic pitching moment and lift defined as: L t Lei t 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.
