<DOC>
<DOCNO>
844
</DOCNO>
<TITLE>
flexural vibrations of the walls of thin cylindrical
shells having freely supported ends .
</TITLE>
<AUTHOR>
arnold,r.n. and warburton,g.b.
</AUTHOR>
<BIBLIO>
proc. roy. soc. a, 197, 1949, 238.
</BIBLIO>
<TEXT>
the paper deals with the general equations for the vibration of thin
cylinders and a theoretical and experimental investigation is made of
the type of vibration usually associated with bells .  the cylinders are
supported in such a manner that the ends remain circular without
directional restraint being imposed .  it is found that the complexity
of the mode of vibration bears little relation to the natural
frequency,. for example, cylinders of very small thickness-diameter
ratio, with length about equal to or less than the diameter, may have
many of their higher frequencies associated with the simpler modes of
vibration .  the frequency equation which is derived by the energy
method is based on strain relations given by timoshenko .  in this
approach, displacement equations are evolved which are comparable to
those of love and flugge, though differences are evident due to the
strain expressions used by each author .  results are given for
cylinders of various lengths, each with the same thickness-diameter
ratio, and also for a very thin cylinder in which the simpler modes of
vibration occur in the higher frequency range .  it is shown that there
are three possible natural frequencies for a particular nodal pattern,
two of these normally occurring beyond the aural range .
</TEXT>
</DOC>
