Refined Mindlin–Reissner theory of forced vibrations of shear deformable plates

Two theories of shear deformable plate vibrations that account for the influence of the transverse normal stress component are derived. The first is a slightly modified Mindlin theory, including a shear correction factor, while in the second the use of the shear correction factor is replaced by stress components that exactly satisfy elasticity motion equations and plate face boundary conditions. A comparison with the exact 3D solution for a sinusoidally loaded rectangular plate and infinite strip is made. It is found that the refined theories significantly increase the accuracy of results compared to the original Mindlin theory.