A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates

In the present paper, a n-order model for functionally graded and composite sandwich plate is developed. This model uses the n-order polynomial term to represent the displacement field. Zero transverse shear stress boundary conditions at the top and bottom of the plate are satisfied. The third-order theory of Reddy [8] can be considered as a special case of present n-order theory. Natural frequencies of the functionally graded and composite plates with various side-to-thickness ratios, material properties are computed by present n-order theory with different n values. The results are compared with available published results which demonstrate the accuracy and efficiency of present n-order theory.

Research Highlights
► A n-order model for functionally graded and composite sandwich plate is developed.
► The third-order theory of Reddy can be considered as a special case of present n-order theory.
► Present theory allows the user to experiment the best order number to approximate the structural problem.