university of florida thesis or dissertation formatting template

Classical aircraft flutter is characterized by the sudden onset of high-amplitude wing
oscillations. It is a self-exciting, dynamic instability of the structural components of the aircraft,
usually involving the coupling of separate vibration modes, where the forcing function for
oscillation is drawn from the airstream. It is often destructive. Linear behavior is represented
well by linear analysis methods.
Classical flutter analyses 7 are accomplished in the frequency domain and involve solving
for the natural vibration frequencies and mode shapes, generalized aerodynamic forces, and
modal damping and frequency variations with velocity. Beginning with the forced vibration
governing equation in the spatial/time domain: 8
[ m]{}
q&
+ []{} c q&
+ []{} k q = { Qˆ
}
& (2-1)
m ]
c ]
[ ]
where [ = mass matrix, [ = damping matrix,
k = stiffness matrix, { q } = displacement
amplitude vector, and the displacement-dependent applied force is given by:
{ Qˆ
1 2 } ρV
[ AIC]{}
q
= (2-2)
2
Linear subsonic aerodynamic influence coefficients (AIC) are computed using the doublet-lattice
method, where the wing surface is discretized into boxes.
Simple harmonic motion is assumed of the form:
{} {} t iω
q q e
= (2-3)
This results in the forced vibration equation in the frequency domain:
2
1 2
( ω [ m]
+ iω[
c]
+ [ k]
){} q = ρV
[ AIC]{}
q
− (2-4)
2
Assuming free vibration in the frequency domain with no applied force and neglecting
damping results in:
2 ( − [ m]
+ [ k]){
q}
= {} 0
ω (2-5)
21