A Cell-Based Smoothed Finite Element Method for Free Vibration Analysis of a Rotating Plate

Abstract

A cell-based smoothed finite element method (CS-FEM) is formulated for nonlinear free vibration analysis of a plate attached to a rigid rotating hub. The first-order shear deformation theory which is known as Mindlin plate theory is used to model the plate. In the process of formulating the system stiffness matrix, the discrete shear gap (DSG) method is used to construct the strains to overcome the shear locking issue. The effectiveness of the CS-FEM is first demonstrated in some static cases and then extended for free vibration analysis of a rotating plate considering the nonlinear effects arising from the coupling of vibration of the flexible structure with the undergoing large rotational motions. The nonlinear coupling dynamic equations of the system are derived via employing Lagrange’s equations of the second kind. The effects of different parameters including thickness ratio, aspect ratio, hub radius ratio and rotation speed on dimensionless natural frequencies are investigated. The dimensionless natural frequencies of CS-FEM are compared with those other existing method including the FEM and the assumed modes method (AMM). It is found that the CS-FEM based on Mindlin plate theory provides more accurate and “softer” solution compared with those of other methods even if using coarse meshes. In addition, the frequency loci veering phenomena associated with the mode shape interaction are examined in detail.