Benchmark solution for free vibration of functionally graded moderately thick annular sector plates

Abstract

In the present article, an exact analytical solution for free vibration analysis of a moderately thick functionally graded (FG) annular sector plate is presented. Based on the first-order shear deformation plate theory, five coupled partial differential equations of motion are obtained without any simplification. Doing some mathematical manipulations, these highly coupled equations are converted into a sixth-order and a fourth-order decoupled partial differential equation. The decoupled equation are solved analytically for an FG annular sector plate with simply supported radial edges. The accurate natural frequencies of the FG annular sector plates with nine different boundary conditions are presented for several aspect ratios, some thickness/length ratios, different sector angles, and various power law indices. The results show that variations of the thickness, aspect ratio, sector angle, and boundary condition of the FG annular sector plates can change the vibration wave number. Also for an FG annular sector plate with one free edge, in opposite to the other boundary conditions, the natural frequency decreases with increasing the aspect ratio for small aspect ratios. Moreover, the mode shape contour plots are depicted for an FG annular sector plate with various boundary conditions. The accurate natural frequencies of FG annular sector plates are presented for the first time and can serve as a benchmark solution.