A two-variable simplified nth-higher-order theory for free vibration behavior of laminated plates

In this article, vibration behavior of composite rectangular plates are investigated by using a refined simple nth-higher-order shear deformation theory. Governing equations are derived by using Hamilton's principle. A closed-form solution via Navier's technique limits the applicability of solution technique to simply-supported rectangular laminated plates. The transverse displacement is dividing into two bending and shear components and so the unknown involved functions is reduced to four, as against five or more in other plate theories. There is no need for any shear correction factors to the present theory. Moreover, it is variationally consistent, used nth-order polynomial term to represent displacement field and gave rise to transverse shear stresses satisfying free surface conditions. Numerical results due to present theory are compared with data available in the literature to show the accuracy and simplicity of the proposed theory in analyzing the vibration frequencies of rectangular orthotropic and laminated composite plates.