THIN-WALLED STRUCTURES, vol.46, no.10, pp.1066-1086, 2008 (SCI-Expanded)
This computational study reports the
free vibration frequencies (corresponding to the first three symmetrical and
antisymmetrical modes), and the minimum buckling load (in case of in-plane
uniform pressure along the periphery) of point-supported super-elliptical plates
of uniform thickness. The plate perimeter was defined by a super-elliptic
function with a power corresponding to the shape ranging from an ellipse to a
rectangle. The analysis was based on the classical theory of thin plates and
the computations were carried out by the Ritz method. The geometrical boundary
conditions were satisfied by the Lagrange multipliers. The results were
compared with those of rectangular plates and good agreement was obtained.