A Survey of Unsteady Hypersonic Flow Problems

- 60 -
.h = -.
q/MA-1
w3 12(1-l?)
Et?
. . . (4.17)
where, for a panel of given shape and loading conditions, h has a fixed value.
It follows that:
t3
9 e
-
9
or -
( ca > cs dz' ( 8" 1 "ii
orit crit
for M large. . . . (4.18)
Then from Fig. 62, at M = 20 and a = 27' (as an example) it can be
seen that the local q/M can be as much as 20 times the free-stream value.
Theoretical predictions of the effect of compressive stress on the flutter of
panels confirm a reduction in flutter dyna ressure with compressive stress
up to the point at which the panel buckles4T79 .
At low supersonic Mach numbers above M= l-4 the boundary layer does
not appear to have very much effect on the flutter characteristics75 but the
very thick boundary layers at hypersonic Mach numbers may have a greater
influence.
(ii) Cylindrical shells
Early analyses had suggeste 46 that large thicknesses were needed to
prevent flutter of cylindrical shells and that the flutter critical thickness
increased quite rapidly with Mach number.
Practical experience has suggested that these results were pessimistio
and this has been confirmed by recent theoretical and experimental work. Early
theoretical investigations, which had not included the effects of material
damping or of damping effects from the boundary layer, had found that the
critical mode of flutter of a finite cylinder was one with no circumferential
nodes. But more recent results published in Ref. 74 show that this mode of
flutter is strongly affected by both material damping and aerodynamic damping and,
as a result, the critical mode becomes one with circumferential nodes and the
critical thickness and dependence on Mach number are considerably reduced. These
results are illustrated by Figs. 64 and 65. The results were confirmed by the
results of experiments reported in Ref. 74.
It can be concluded, then, that for cylindrical shells, as for flat
panels, the perfect fluid dynamic effects of high Mach number are not likely to
cause any important changes in the flutter conditions, but there will be
important effects in practice from heating of the structure causing reductions
in material properties and compressive stresses, from the local flow conditions,
and from the influence of the thick boundary layers. It seems likely that the
effect of the thick hypersonic boundary layers will still be stabilising but
some investigation of this i‘s needed.
4.3 Discussion and Conclusions
From the information which has been collected in this review, it seems
likely that the principal causes of any degradation of flutter behaviour on
vehicles operating at hypersonic speeds will be the degradation of the stiffness
properties of the structure and the high local values of dynamic pressure, rather
than any large changes in fluid dynamic behaviour.
Most/