A nth-order shear deformation theory for natural frequency of the functionally graded plates on elastic foundations

Natural frequencies of functionally graded plates resting on elastic foundation are calculated using a nth-order shear deformation theory and a meshless approach. The present theory is a nth-order generalization of Reddy's third-order shear deformation theory. This theory does not require shear correction factor, and satisfies the zero transverse shear stress boundary conditions on the top and bottom surface of the plate. The elasticity modulus and density of the functionally graded plates are assumed to vary continuously through the thickness direction according to power law distribution of the volume fraction of the constituents. Governing equations are derived from the principle of virtual displacements. The meshless solutions are presented and compared with the available accurate solutions to verify the validity of the present theories.