Three-dimensional elasticity solutions to vibration of cantilevered skewed trapezoids

An accurate three-dimensional elasticity model for determining the free vibration response of skewed trapezoidal plates is presented. The method is formulated on the basis of a linear, small-strain, three-dimensional elasticity theory with the Ritz minimization procedure. The solution method uses sets of uniquely defined one- and two-dimensional polynomial functions to approximate the trial displacements in the thickness and surface directions, respectively. These functions are orthogonally generated and have been proven to be highly efficient and numerically stable. The proposed technique yields natural frequencies and mode shapes for a wide range of cantilevered skewed trapezoidal plates of arbitrary planform. The accuracy of these results, whenever possible, is validated through comparison with the analytical and experimental data. Parametric investigations on the vibration behavior of cantilevered trapezoidal plates with respect to different thickness ratios, skew angles, and chord ratios have been carried out. For the first time, the presence of surface parallel symmetric thickness modes for these plates is demonstrated in vivid three-dimensional mode shape plots.