<DOC>
<DOCNO>
1392
</DOCNO>
<TITLE>
the solution of small displacement, stability or vibration
problems concerning a flat rectangular panel when the
edges are either clamped or simply supported .
</TITLE>
<AUTHOR>
hopkins,h.g.
</AUTHOR>
<BIBLIO>
arc r + m.2234, 1945.
</BIBLIO>
<TEXT>
  this report describes an energy method for
the exact solution of problems concerning the small
displacements, stability or vibration of a flat rectangular panel
when the edges are either clamped or simply supported .
the influence of stiffeners which are parallel to one pair of edges,
and situated in pairs on opposite sides of the panel
so that the neutral axis of each stiffener pair lies in the middle
surface of the panel, is taken into account .  the method
is not only applicable to isotropic panels but also to aeolotropic
panels when the material of the panel has two directions
of elastic symmetry parallel to the edges .
  the final solution of the problems depends on an infinite set of
linear equations for small displacement problems or on
an infinite determinantal equation for stability and vibration
problems .  the important feature of the analysis given is
that it enables a direct approach to be made to these equations
in any particular problem .  it is not in general possible
to obtain a direct solution of the final equations and it is
necessary to approximate and consider a finite set of linear
equations or a finite determinantal equation derived from the
more important terms in the analytical expression for the
transverse displacement of the panel .  here, physical intuition
and, if available, experimental data serve as a guide and
the accuracy of the final results so obtained is gauged by the
rate of convergence with the increase in the number of
terms considered .
  the general method of solution is applied first to the free
vibration of a square panel when all the edges are clamped,
and second to the buckling of a square panel under shear when
three edges are clamped and one edge is simply supported .
</TEXT>
</DOC>
