Study of effects of sweep on the flutter of cantilever wings Page: 2 of 25
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.REPORT 1014-NATIONAL ADVISORY COMMITTEE FOR. AERONAUTICS
of flutter involving sweep are R. 'McKinnon Wood, A. R.
Collar, and I. . Minin nick. An account of MIinhinnick's
work was given by Broadbent in reference 2. In reference 3
a preliminary analysis for the flutter of swept wings in
incompressible flow is developed on the basis of a "strip
theory" (with the strips taken in the stream direction) and
is applied to the experimental results of reference 1. Exam-
ination of the limiting case of infinite span discloses that
the aerodynamic assumptions employed in reference 3
are not well-grounded. Reference 4 adapts this strip
theory to flexible wings and also presents an alternative
"velocity component" treatment employing other aerody-
namic assumptions which in their end result appear more
akin to those employed in the analysis of the present report.
No definite choice is made in reference 4 between the two
methods although the strip-theory method is favored.
In the present report a theoretical analysis is developed
anew and given a general presentation. Application of the
analysis has been limited at this time chiefly to those calcu-
lations needed for comparison with experimental results.
A wider examination of the effect of various parameters
and of additional degrees of freedom on the flutter character-
istics is desirable.
SYMBOLS
b half-chord of wing measured perpendicular to
elastic axis, feet
b, half-chord perpendicular to elastic axis at
reference station, feet
i' effective length of wing, measured along
elastic axis, feet
c wing chord measured perpendicular to elastic
axis, inches
l length of wing measured along midchord line,
inches
A angle of sweep, positive for sweepback, degrees
A, geometric aspect ratio (( cos A)'
X' coordinate perpendicular to elastic axis in
plane of wing, feet
y' coordinate along elastic axis, feet
z' coordinate in direction perpendicular to
x'y'-plane, feet
Z coordinate of wing surface in z'-direction, feet
77 nondimensional coordinate along elastic axis
(y'/1')
coordinate in wind-stream direction
h bending deflection of elastic axis, positive
downward, feet
O torsional deflection of elastic axis, positive
with leading edge up, radians
U local bending slope of elastic axis ( , )fA(y'), Fh(n)
fo(y') Fe(,)
tlocal rate of change of twist b-1)
deflection function of wing in bending
deflection function of wing in torsion
time
angular frequency of vibration, radians per
secondwe
fl,'
ft
fix
fe
fR
fiA
V
aeVR
V',
V,
k,
P
q
M
Xc,
Xa
zeaa
a + x.
m
K
leeangular uncoupled bending frequency, radians
per second
angular uncoupled torsional frequency about
elastic axis, radians per second
first bending natural frequency, cycles per
second
second bending natural frequency, cycles
per second
first torsion natural frequency, cycles per
second
uncoupled first. torsion frequency relative to
elastic axis, cycles per second
(s./r.)' 1
experimental flutter frequency, cycles per
second
reference flutter frequency, cycles per second
flutter frequency determined by analysis of
present report, cycles per second
free-stream velocity, feet per second
experimental flutter speed, feet per second
component of air-stream velocity perpen-
dicular to elastic axis, feet per second
(v cos A)
experimental flutter speed taken parallel to
air stream, miles per hour
reference flutter speed, miles per hour
reference flutter speed based on wing elastic
axis, miles per hour (defined in appendix B)
flutter speed determined by theory of present
report, miles per hour
theoretical divergence speed, miles per hour
reduced frequency employing velocity com-
ponent perpendicular to elastic axis (wb/v,)
phase difference between wing bending and
wing torsion strains, degrees
density of testing medium at flutter, slugs per
cubic foot
dynamic pressure at flutter, pounds per square
foot
Mach number at flutter
critical Mach number
distance of center of gravity behind leading
edge taken perpendicular to elastic axis,
percent chord
distance of elastic center of wing cross section
behind leading edge taken perpendicular to
elastic axis, percent chord
distance of elastic axis of wing behind leading
edge taken perpendicular to elastic axis,
percent chord
/2x,
nondimensional elastic-axis position \ f 1
nondimensional center-of-gravity position
100-1mass of wing per unit length, slugs per foot
wing mass-density ratio at flutter (rp b'/m)
mass moment of inertia of wing per unit length
about elastic axis, slug-feet2 per foot230
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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/m1/2/: accessed November 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.