Study of effects of sweep on the flutter of cantilever wings Page: 13 of 25
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STUDY OF EFFECTS OF SWEEP ON THE FLUTTER OF CANT ILEVER WINGS
were loaded at points lying in the chordwise direction. The
point for which pure bending deflection occurred, with no
twist in the plane normal to the leading edge, was determined.
The same procedure was used for those wings which were
clamped at the root, not normal, but at an angle to the
leading edge. A different elastic axis designated the "wing"
elastic axis and located at x,,' was thus determined.
For these uniform, swept wings with fairly large length-
chord ratios, the wing elastic axis was reasonably straight
and remained essentially parallel to the section elastic axis,
although it was found to move farther behind the section
elastic axis as the angle of sweep was increased. It is real-
ized that in general for nonuniform wings-for example,
wings with cut-outs or skewed clamping-a certain degree
of cross stiffness exists and the concept of an elastic axis is
an oversimplification. More general concepts such as those
involving influence coefficients may be required. These
more strict considerations, however, are not required here
since the elastic-axis parameter is of fairly secondary impor-
The wing mass-density ratio K is the ratio of the mass of a
cylinder of testing medium, of a diameter equal to the chord
of the wing, to the mass of the wing, both taken for unit
length along the wing. The density of the testing medium
when flutter occurred was used in the evaluation of x.
Determination of the reference flutter speed.-It is
convenient in presenting and comparing data of swept and
unswept wings to employ a certain reference flutter speed.
This reference flutter speed will serve to reduce variations
in flutter characteristics which arise from changes in the
various model parameters such as density and section proper-
ties not pertinent to the investigation. It thus aids in
systematizing the data and emphasizing the desired effects
of sweep including effects of aspect ratio and Inach number.
This reference flutter speed It may be obtained in the
following way. Suppose the wing to be rotated about the
intersection of the elastic axis with the root to a position of
zero sweep. In this position the reference flutter speed is
calculated by the method of reference 7, which assumes an
idealized, uniform, infinite wing mounted on springs in an
incompressible medium. For nonuniform wings, a reference
section taken at a representative spanwise position, or some
integrated value, may be used. Since the wings used were
uniform, any reference section will serve. The reference
flutter speed may thus be considered a "section" reference
flutter speed and parameters of a section normal to the Iead-
ing edge are used in its calculation. This calculation also
employs the uncoupled first bending and torsion frequencies
of the wing (obtained from the measured frequencies) and
the measured density of the testing medium at time of
flutter. The calculation yieIds a corresponding reference
flutter frequency which is useful in comparing the frequency
data. For the sake of completeness a further discussion of
the reference flutter speed is given in appendix B.
Test procedure and records.-Since flutter is often a
sudden and destructive phenomenon, coordinated test pro-
cedures were required. During each test, the tunnel speed
was slowly raised until a speed was reached for which the
amplitudes of oscillation of the model in bending and torsion
increased rapidly while the frequencies in bending and tor-
sion, as observed on the screen of the recording oscillograph,
merged to the same value. At this instant, the tunnel
conditions were recorded and an oscillograph record of the
model deflections was taken. The tunnel speed was im-
mediately reduced in an effort to prevent destruction of the
From the tunnel data, the experimental flutter speed I,,
the density of the testing medium p, and the ach number M1
were determined. No blocking or wake corrections to the
measured tunnel velocity were applied.
From the oscillogram the experimental flutter frequency
f, and the phase difference jp (or the phase difference -1800)
between the bending and torsion deflections near the root
were read. A reproduction of a typical oscillograph flutter
record, which indicated the flutter to be a coupling of the
wing bending and torsion degrees of freedom, is shown as
figure 4. Since semispan wings mounted rigidly at the base
were used, the flutter mode may be considered to correspond
to the flutter of a complete wing having a very heavy fuselage
at midspan-that is, to the symmetrical type.
The natural frequencies of the models in bending and
torsion at zero airspeed were recorded before and after each
test in order to ascertain possible changes in structural char-
acteristics. In most cases there were no appreciable changes
in frequencies but there were some reductions in stiffnesses __
for models which had been weakened by fluttering violently.
Analysis of the decay records of the natural frequencies
indicated that the wing damping coefficients g and g,
(reference 7) were about 0.02 in the first bending mode and
0.03 in the torsion mode.
RESULTS AND DISCUSSION
Presentation of experimental data.-Results of the
experimental investigation are listed in detail in tables I to
VTI, and some significant experimental trends are illustrated
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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/m1/13/: accessed February 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.