Free linear vibration and buckling of super-elliptical plates resting on symmetrically distributed point-supports on the diagonals

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.