Higher-order shear and normal deformable theory for functionally graded incompressible linear elastic plates

We use the principle of virtual work to derive a higher-order shear and normal deformable theory for a plate comprised of a linear elastic incompressible anisotropic material. The theory does not use a shear correction factor and employs three components of displacement and the hydrostatic pressure as independent variables. For a KKth order plate theory, a set of 4(K+1)4(K+1) coupled equations need to be solved for the (K+1)(K+1) pressures and the 3(K+1)3(K+1) displacements defined on the reference surface of the plate.Equations for free vibrations of a plate are derived, and equations for the determination of frequencies and the corresponding mode shapes of a simply supported rectangular plate are given.