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1.10. Supplement on Lumped Mass of the Vibrating Wing
For the wing tip plucking experiment, each point along the wing is moving with some
velocity.
We can derive an equivalent vibrating mass (lumped mass) located at the end
of the wing by integrating the kinetic energy in the motion of every point along the wing.
1.
The static wing deflection equation gives a relationship between the end deflection
and any other point.
With
x
measured from the wing end,
x=L
is the base where the
wing meets the fuselage.
From strength of materials textbooks, the end deflection due
to a point load,
F
, at the end of a cantilevered wing depends on the material’s modulus
of elasticity,
E
, bending moment of inertia,
I
, and wing length,
L
, is (defining a unitless
x
coordinate)
2.
The maximum deflection is at the wing end (
=0) where the point force is applied and
the minimum deflection is at the clamped end (
=1)
then the deflection at any point along the wing in terms of the end deflection is
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This note was uploaded on 02/07/2011 for the course AE/ME 301 taught by Professor Lafleur during the Spring '11 term at Clarkson University .
 Spring '11
 LaFleur

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