M. K. AHMED
Copyright © 2011 SciRes. AM
Figure 8. Buckling loads versus axial half wave number of a
three-lobed cross-section cylindrical shell with variable thi-
ckness. (=0.3,= 0.02νh).
by using the transfer matrix method. The method is
based on thin shell theory and applied to a shell of sym-
metric and antisymmetric vibration modes, and the anal-
ysis is formulated to overcome the mathematical difficul-
ties associated with mode coupling caused by variable
shell wall curvature and thickness. The first five funda-
mental frequencies and mode shapes as well as critical
buckling loads have been presented, and the effects of
the thickness ratio of the cross-section on the natural fre-
quencies, mode shapes, and buckling loads were exa-
mined. For the thickness ratio 1
, the vibration mod-
es are distributed regularly over the shell surface, but for
the modes are localized near the weakest genera-
, (thinner edge), in most cases of the vibration
modes. However, the critical buckling loads increase
with either increasing radius ratio or increasing thickness
ratio and become larger for a circular cylindrical shell.
For the cylindrical shell of (1
), the criti-
cal loads are occurred with 2m
, but for the shell un-
der consideration of (1
) they occurred
with 3m for the symmetric and antisymmetric vibra-
The author is grateful to anonymous reviewers for their
good efforts and valuable comments which helped impr-
ove the quality of this paper.
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