<DOC>
<DOCNO>
845
</DOCNO>
<TITLE>
the flexural vibrations of thin cylinders .
</TITLE>
<AUTHOR>
arnold,r.n. and warburton,g.b.
</AUTHOR>
<BIBLIO>
j. proc. i. mech. e. 167, 1953, 62.
</BIBLIO>
<TEXT>
the flexural vibrations of the walls of thin cylinders are considered .
in this type of vibration many forms of nodal pattern may exist owing to
the combination of circumferential and axial nodes .  theoretical
expressions are developed for the natural frequencies of cylinders with
freely-supported and fixed ends and a comparison is made with the
frequencies obtained experimentally .
  in practice, the ends of cylinders are subjected to a certain degree
of fixing by end-plates, flanges, etc., and the natural frequencies thus
lie between the corresponding values for freely-supported and fixed
ends .  to make possible the estimation of such frequencies, a method is
devised in which an equivalent wavelength factor is used .  this factor
represents the wavelength of the freely-supported cylinder that would
have the same frequency as the cylinder under consideration when
vibrating in the same mode .  the results of experimental investigations
with various end thicknesses and flange dimensions are recorded, and
from these the equivalent factors are derived .
  sets of curves calculated for cylinders with freely-supported ends and
covering a range of cylinder thicknesses are given .  from these it is
possible to obtain close approximation to the frequencies of cylinders
under other end conditions by the use of an appropriate factor .  an example
is given of frequency calculations for a large air-receiver for
which two frequencies were identified by experiment .
</TEXT>
</DOC>
