A Survey of Unsteady Hypersonic Flow Problems

- 59 -
The conclusion drawn from Fig. 58 is supported by the results shown
in Wg. 59 for a.geometrically similar cone mth different axis Position and
c.g. position, at M = 2, 3 and 6.83. There is rather more scatter of the
experimental points, but there is still .e strong suggestion that the flutter of
the cone is not greatly affected by Mach number. Calculations by Newtonian
theory and by shock expansion theory were made for the M = 6.83 ease, but only
poor agreement was obtained. The shock expansion result is not shown in Fig. 58.
The failure of the analysis using shock expansion theory in Ref. 63
may be related to the fact that the flow is predominantly conical, despite the
unsteady oomponents, and such flows violate a condition for the use of shock
expansion theory for three-dimensional bodies.
For the flutter cases in both Figs. 58 and 59 the analysis was found
to be affected by the inclusion of e factor from the drag of the cone. The
qualitative effect of this is shown by one curve in each Figure.
The large variations of flutter parameter shown in Fig. 57 for axes
around the mid-length are not shown in Figs. 58 and 59. This may be related
to the particular theory used since the results of applying van Karman s theory
in Ref. 63 also showed a dependence of critical flutter parameter on Mach number.
But direct comparisons are not possible because of the different characteristics
of the cones used: the frequency ratio of &ma = 0.5, used in the investigations
.for Fig. 57, was not investigated in Ref. 63 and, in fact, Figs. 58 and 59 suggest
that flutter would not have been possible at a frequency ratio of O-5 for the
models used in those investigations.
4.2.3 Panel flutter
There appear to be no published results of investigations of panel
flutter at hypersonic speeds but, since it can be assumed from structural
considerations that displacements will remain very small, the hypersonic
similarity parameter for the displacements, M6, will remain small, and
consequently It is reasonable to draw tentative conclusions about panel flutter
at hypersonic speeds by extrapolation from experiments and piston theory analyses
for lower Mach numbers. This is the basis on which this section has been
written. Surveys of information on panel flutter at lower M&ch numbers are given
in Refs. 74 and 76.
(i) Flat panels
Analyses for Mach numbers between 2 and 5 indicate that the effects
of changes in the fluid dynamics of a perfect gas due to increased Mach number
do not cause a significant change in the critical thickness ratio for flutter
This is illustrated by Figs. 60 and 61, from Refs. 69 and 70, for a buckled
two-dimensional panel clamped front and rear, and for B rectangular panel simply
supported on all four edges. These results show, for Mach numbers greater than
about 1.2, a small increase in critical thickoess with increasing Mach number.
But there are two effects occurring in real flight situations which cald make
panel flutter B significant problem at hypersonic speeds. These effects are the
large increases of dynamic pressure which can ocour in the local flow conditions
on vehicles, especially on the lifting surfaces of vehicles at large angles of
attack and in intake ducts; and aerodynamic heating effects, which would lower
the elastic stiffness and could set up OODpreSSive stresses in Panels, or even
oause buckling. 'Pyplcal local flow con&Cons which could occur are shown In
Fig. 62 from Ref. 71. The significance of the conditions can be gauged from the
critical dynamic Pressure parameter h found by Hedgepeth in Ref. 70:
h/