FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED ANNULAR SECTOR PLATES BY THE EXTENDED KANTOROVICH METHOD

In this paper, free vibration of functionally graded (FG) annular sector plates is studied using the extended Kantorovich method (EKM). To this end, based on the first-order shear deformation theory (FSDT) and Hamilton's principle, the equations of motion which are five coupled partial differential equations in terms of five displacement field variables are derived. By applying the EKM, the governing equations are reduced to two sets of ordinary differential equations in radial and circumferential directions which are solved using generalized differential quadrature method (GDQM) and state-space method, respectively. Natural frequencies are obtained through an iterative process for FG sector plates with different types of clamped and simply supported boundary conditions at the radial and circumferential edges. The results are validated by comparison with the existing ones in the literature. Finally, the effect of various parameters such as boundary conditions, material constants, and geometric parameters of the plate on the natural frequencies of FG annular sector plates is investigated. This is the first time that the EKM is used for vibration analysis of plates in polar coordinate. It is shown that the method has high accuracy and convergence for vibration analysis of plates in polar coordinate, similar to its performance in Cartesian coordinate. In addition, it is concluded that the initial guess, as the first approximation for the solution, has no effect on the final results. Furthermore, it is observed that increasing the sector angle reduces the natural frequencies while increasing the plate thickness increases them (reduces the non-dimensional natural frequencies introduced in this paper) due to the increasing plate rigidity. This effect is more pronounced in higher modes rather than the lower ones. Finally, the natural frequencies presented via a semi-analytical method for FG annular sector plates with various boundary conditions, material constants, and geometric parameters can be used as a benchmark for future studies.