A nth-order meshless generalization of Reddy’s third-order shear deformation theory for the free vibration on laminated composite plates

In this paper, a nth-order shear deformation theory is proposed to analyze the free vibration of laminated composite plates. The present nth-order shear deformation theory satisfies the zero transverse shear stress boundary conditions on the top and bottom surface of the plate. Reddy’s third-order theory can be considered as a special case of present nth-order theory (n = 3). Natural frequencies of the laminated composite plates with various boundary conditions, side-to-thickness ratios, material properties are computed by present nth-order theory and a meshless radial point collocation method based on the thin plate spline radial basis function. The results are compared with available published results which demonstrate the accuracy and efficiency of present nth-order theory.