<DOC>
<DOCNO>
1036
</DOCNO>
<TITLE>
on transverse vibrations of thin, shallow elastic shells .
</TITLE>
<AUTHOR>
reissner,e.
</AUTHOR>
<BIBLIO>
q. app. math., 13, 1955, 169.
</BIBLIO>
<TEXT>
  according to marguerre (proc. 5th internat. congress
appl. mech., cambridge, mass., 1938, wiley, new york,
shells are governed by three simultaneous differential equations
in the three displacements .  the author has considerably
simplified this theory for the case of transverse vibrations
by ignoring the longitudinal inertia terms, thus reducing
the problem to that of solving two simultaneous
differential equations in a stress function and one displacement
component .  this simplification is justified by an orderof-magnitude
analysis, and illustrated by considering the
vibrations of a paraboloidal shell with a rectangular
boundary .
</TEXT>
</DOC>
