A comparison of the non-conforming and conforming sector finite element for free vibration of circular discs

Abstract

A twelve-term non-conforming and a sixteen-term conforming displacement polynomial are obtained from Pascal's triangle to deduce the shape functions for a sector element. Using the sector element circular disc is discretized. The number of degrees of freedom for the sector element at a given node is three and four. Kirchhoff's plate theory is the basis for strain energy and kinetic energy because of the transverse motion of the circular plate. Associated stiffness and mass matrices for the sector element are derived in closed form using MATHEMATICA. Using the Lagrange equation, the free vibration equation of motion for the circular disc is derived. A validation study is conducted, and non-dimensional frequencies from the finite element solution are compared with the analytical solutions reported in the literature. Subsequently, the natural frequencies of Al-Al<inf>2</inf>O<inf>3</inf>functionally graded circular disc with gradation in the thickness direction are evaluated for a variety of boundary conditions. © 2020 Elsevier Ltd. All rights reserved.