Single-layer plate theories applied to the flexural vibration of completely free thick laminates

Two different refined single-layer plate theories are used to analyze the flexural vibration of thick symmetrically laminated rectangular plates with all edges free. Both theories account for parabolic distribution of the transverse shear strains through the thickness of the plate. The first theory includes the transverse normal effect and employs a three-dimensional constitutive law, whereas the second neglects this effect and employs plane-stress reduced stiffnesses. Numerical results are obtained by using the Ritz method. Characteristic orthogonal polynomials are used in the series representing the displacement functions. Convergence studies are shown to verify the accuracy of the approximate method. The accuracy of the results is further assessed by comparison with results from three-dimensional finite element analyses. Numerical results are presented for various plates including cross-ply and angle-ply laminated plates. The effect of transverse shear and normal deformation on the plate natural frequencies is illustrated by comparing the frequencies of the two higher order theories and the classical plate theory for decreasing length-to-thickness ratio.