Natural vibrations of shear deformable cantilevered skew thick plates

The natural vibrations of thick and thin cantilevered skew plates are analyzed using C⁰ continuous finite element assemblages of nine-node Lagrangian isoparametric quadrilateral plates based on three shear deformable thick plate theories. Finite elements based on the widely used first order Reissner-Mindlin plate theory are compared to those derived from two higher order shear deformable plate theories. Here, additional nodal displacement degrees of freedom are derived by retaining higher order powers of the thickness coordinate in the in-plane displacement fields. Essential rotary inertia terms are derived and included in the present analysis. An extensive amount of non-dimensional frequencies and mode shapes are calculated for thick and thin skew cantilevered plates having various thickness ratios and arbitrary degrees of skewness. The efficacy of using higher order shear deformable plate finite elements for predicting the in-plane vibration modes of skew plates is found to increase as the thickness ratio decreases and the skew angle increases. The present work shows that higher order shear deformable finite elements essentially eliminate the over-correction of thick skew plate frequencies that is produced when first order shear deformable finite elements are utilized. Results using the present finite element analysis are compared with those obtained using three-dimensional finite element and continuum-based analyses, and experimental methods.