Three-dimensional free vibration analysis of perforated super elliptical plates via the p-Ritz method

A three-dimensional free vibration analysis of a perforated plate with rounded corners is presented. A solution method based on the linear, small strain, three-dimensional elasticity theory and the p-Ritz algorithm is employed. This analysis method uses sets of uniquely defined one- and two-dimensional polynomial functions as the trial displacements in the thickness and surface directions to arrive the eigenvalue equation which yields the natural frequencies and mode shapes for the perforated super elliptical plates. The accuracy of these results, if possible, is validated through comparison with the available literature. Parametric investigations on the vibration behaviours of the perforated super-elliptical plates with respect to different thickness ratios, cutout sizes and boundary constraints are examined.