Three-dimensional free vibration analysis of perforated super-elliptical plates via \(p\)-Ritz method. (Q5954230)

A three-dimensional free vibration analysis of a perforated plate with rounded corners is presented. A solution based on linear, small strain, three-dimensional elasticity theory and the \(p\)-Ritz algorithm is employed. This analysis method uses the sets of uniquely defined one- and two-dimensional polynomial functions as trial displacements in the thickness and surface directions to arrive at the eigenvalue equation which yields the natural frequencies and mode shapes for perforated elliptical plates. Accuracy of these results is validated through comparison with available literature.