Vibration and Buckling Analysis of Functionally Graded Plates Using New Eight-Unknown Higher Order Shear Deformation Theory

Abstract

In this paper a new eight-unknown higher order shear deformation theory is proposed to study the buckling and free vibration of functionally graded (FG) material plates. The theory bases on full twelve-unknown higher order shear deformation theory, simultaneously satisfies zero transverse shear stress at the top and bottom surfaces of FG plates. Equations of motion are derived from Hamilton's principle. The critical buckling load and the vibration natural frequency are analyzed. The accuracy of present analytical solution is confirmed by comparing the present results with those available in existing literature. The effect of power law index of functionally graded material, side-to-thickness ratio on buckling and free vibration responses of FG plates is investigated.

Keywords:
Buckling; vibration analysis; functionally graded materials; higher order shear deformation theory; closed-form solution