Free Vibration Analysis of Spinning Sandwich Annular Plates with Functionally Graded Graphene Nanoplatelet Reinforced Porous Core

Abstract

This paper conducted the free vibration analysis of a sandwich annular thin plate with whirl motion. The upper and lower faces of the annular plate are made of uniform solid metal, while its core is porous foamed metal reinforced by graphene nanoplatelets (GPLs). Both uniform and non-uniform distributions of GPLs and porosity along the direction of plate thickness which leads to a functionally graded (FG) core are taken into account. The effective material properties including Young’s modulus, Poisson’s ratio and mass density are calculated by employing the Halpin–Tsai model and the rule of mixture, respectively. Based on the Kirchhoff plate theory, the differential equations of motion are derived by applying the Lagrange’s equation. Then, the assumed mode method is utilized to obtain free vibration behaviors of the sandwich annular plate. The finite element method is adopted to verify the present model and vibration analysis. The effects of porosity coefficient, porosity distribution, graphene nanoplatelet (GPL) distribution, graphene nanoplatelet (GPL) weight fraction, graphene nanoplatelet length-to-thickness ratio (GPL-LTR), graphene nanoplatelet length-to-width ratio (GPL-LWR), spinning speed, outer radius-to-thickness ratio and inner radius-to-thickness ratio of the plate, are examined in detail.