Study of effects of sweep on the flutter of cantilever wings Page: 20 of 25
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APPENDIX B
DISCUSSION OF THE REFERENCE FLUTTER SPEEDFor use in comparing data of swept and unswept wings, a
reference flutter speed V1 is convenient. This reference
flutter speed is the flutter speed determined from the simpli-
fied theory of reference 7. This theory deals with tNwo-
dimensional unswept wings in incompressible flow and de-
pends upon a number of wing parameters. The calculations
in this report utilize parameters of sections perpendicular to
t le leading edge, first bending frequency, uncoupled torsion
frequency, density of testing medium at time of flutter, and
zero damping. Symbolically,
VR=bwcf(KXcxieatrc 2 )
Variation in reference flutter speed with sweep angle for
sheared swept wings.-The reference flutter speed is
independent of sweep angle for a homogeneous rotated wing
and for homogeneous wings swept back by keeping the length-
chord ratio constant. For a series of homogeneous wings
swept back by the method of shearing, however, a definite
variation in reference flutter speed with sweep angle exists
since sweeping a wing by shearing causes a reduction in
chord perpendicular to the wing leading edge and an increase
in length along the midchord as the angle of sweep is in-
creased. The resulting reduction in the mass-density-ratio
parameter and first bending frequency tends to raise the
reference flutter speed, whereas the reduction in semichord
tends to lower the reference flutter speed as the angle of
sweep is increased. The final effect upon the reference
flutter speed depends on the other properties of the wing.
The purpose of this section is to show the effect of these
changes on the magnitude of the reference flutter speed for
a series of homogeneous sheared wings having properties
similar to those of the sheared swept models used in thiis
report.
Let the subscript 0 refer to properties of the wing at zero
sweep angle. The following parameters are then functions
of the sweep angle:
b=bo cos A
cos A
248Since m is proportional to b,
brp 2
K= -= K cos A
Sinfilarly, since I is proportional to b,
0.56 I,
f, =--v- = (a)o(cos A)2
Also, because f, is independent of A,
h (cos A)'
An estimate of the effect on the flutter speed of these
changes in semichord and mass parameter with sweep angle
may be obtained from the approximate formula given in
reference 7,
V r, 0.5
VE - i 0.5+a+xm -=8 os A
This approximate analysis of the effect on the reference
flutter speed does not depend upon the first bending frequency
but assumesfh/f. to be small.
In order to include the effect of changes in bending-torsion
frequency ratio, a more complete analysis must be carried
out. Figure 20 presents some results of a numerical analysis
based on a homogeneous wing with properties at zero sweep
angle as. follows:x.,=50
x,.= 45
r '- 0.25
f,= 100bo=0.333
(D= 10
( -=0.4In figure 20 the curve showing the decrease in V, with A is
slightly above the /cos A factor indicated by the approxi-
mate formula.
Effect of elastic-axis position on reference flutter speed.-
As pointed out in the definition of elastic axis, the measured
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Barmby, J G; Cunningham, H J & Garrick, I E. Study of effects of sweep on the flutter of cantilever wings, report, January 1, 1951; (digital.library.unt.edu/ark:/67531/metadc60354/m1/20/: accessed December 15, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.