Budding and free vibration of elastic plates using simple and mixed shear deformation theories

Simple and mixed shear deformable theories accounting for the transverse sh ear, in the sense of Reissner-Mindlin's thick plate theory, are employed in the construction of variational statements for rectangular flat plates. An alytical solutions for natural frequencies and buckling loads of anisotropi c plates under various boundary conditions are developed. A variety of simp ly-supported, clamped and free boundary conditions is considered, and compa risons with the existing literature are made.