Natural frequencies of shear deformable rhombic plates with clamped and simply supported edges
The natural vibrations of thick and thin rhombic plates with clamped and simply supported edges are analyzed, using assemblages of nine-node Lagrangian isoparametric quadrilateral \(C^ 0\) continuous finite elements, and using a higher-order shear deformable thick plate theory. Here, additional nodal displacement degrees of freedom are derived by retaining higher-order powers of the thickness coordinate in the in-plane displacement fields, wihch in turn allows for the proper representation of the transverse shear strains of thick plates. Essential rotary inertia terms are derived and included in the present analysis. Nondimensional frequencies are calculated for thick and thin rhombic plates having various combinations of clamped and simply supported edge conditions, and skew angles. The efficacy of using higher-order shear deformable plate finite elements for predicting the in-plane vibration modes of rhombic plates is found to increase as the span-to-thickness ratio decreases and the skew angle increases. The work shows that higher- order shear deformable finite elements essentially eliminate the transverse shear over-correction of thick rhombic plate frequencies, that is produced when finite elements based on the widely used first-order Reissner-Mindlin plate theory are used.
nine-node Lagrangian isoparametric quadrilateral elements
higher-order shear deformable thick plate theory
scientific article; zbMATH DE number 755003