Three-dimensional free vibration analysis of plates using the h-p version of the finite element method

The h-p version of the finite element method based on a pentahedral p-element is applied to three-dimensional free vibrations of plates. The element's new hierarchical shape functions are expressed in terms of the shifted Legendre orthogonal polynomials. The accuracy of the solution can be improved by simultaneously refining the mesh and increasing the polynomial order. The method is capable of providing a full frequency spectrum including both the in-plane and the out-of-plane modes. Results of frequency calculations are first found for a skew plate on a soft edge support and a cantilevered right isosceles triangular plate and comparisons are made with other methods. Results are also found for a square plate on a hard edge support and comparisons are made with two-dimensional plate theories. Furthermore, highly accurate values for a free hexagonal plate are presented for the first time.