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Flutter Analysis

806 words - 4 pages

March 14, 2012

[AEROELASTICITY MIDTERM PROJECT-FLUTTER ANALYSIS ]

Objective:
To conduct flutter analysis of a typical section model of an airfoil using the parameters as
discussed in lecture. Consider both the case without the

̇

̇

term and the case with the term in

the aerodynamic model. Create the Eigen value plot for both the cases.
Answer:
Introduction to 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, ...view middle of the document...

If the real part of any value of ‘p’ is positive then
the motion diverges exponentially with time and the typical section is unstable.
Substituting E3 into E1 and E2 we obtain:
̅

̅

̅

̅

̅

̅

̅

(E4)
̅

(E5)

Equations E4 and E5 can be represented in the following matrix form after eliminating
̅
[ ]{ }
̅
[]

where,

{}

[

]

For non-trivial solution, det [D] = 0:
(

(

)

(

)

Page 2

:

[AEROELASTICITY MIDTERM PROJECT-FLUTTER ANALYSIS ]

March 14, 2012

Rearranging the equation:
(

)

(

)

(

)

(E6)

Given that (unit ommitted):
b=1,

, c=2, M=1,

5,

Solving E6 with Matlab by assumming,

FIG.1
FIG. 1 shows a representation of the imaginery and real parts of the eigenvalue for case without
additional term in the aerodynamic damping. The point at which
changes from negative to
positive gives us critical value of
at which flutter occurs.

Page 3

[AEROELASTICITY MIDTERM PROJECT-FLUTTER ANALYSIS ]

March 14, 2012

̇

Case 2: Flutter Analysis when additional term is persent in the aerodynamic damping ( )
̇

The equations of motion for the damped case (with the term)
̈

̇

̈

̇

̈
̈

(E7)
(E8)

Let us assume the motion to be simple harmonic
̅

̅

(E9)

where,
and
The factor ‘
’ gives the frequency of oscillation of the system, whereas ‘
’ represents the
growth or decay of the system with time. Again, if the real part of any value of ‘p’ is positive
then the motion diverges exponentially with time and the typical section is unstable.
Substitute E9 into E7 and E8 to obtain:
̅

̅

̅

̅

̅

̅

̅

̅

(E10)
̅

̅

(E11)

Equations E10 and E11 can be represented in the following matrix form after...

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