Eur. Phys. J. Plus (2021) 136: 147
https://doi.org/10.1140/epjp/s13360-021-01131-6

Regular Article

Coupled free vibration analysis of functionally graded shaft-disk system by differential quadrature finite element method

¹ College of Mechanical and Electrical Engineering, Central South University, 410083, Changsha, People’s Republic of China
² State Key Laboratory of High Performance Complex Manufacturing, Central South University, 410083, Changsha, People’s Republic of China

^b wangqingshanxlz@hotmail.com

Received: 16 September 2020
Accepted: 16 January 2021
Published online: 28 January 2021

Abstract

The purpose of this paper is to investigate coupling vibration characteristics of the flexible functionally graded material (FGM) shaft-disk coupling system with variable thickness disk. The mathematical model of the shaft-disk system is based on the first-order shear deformation theory, combined with the Voigt model and the four-parameter power-law distribution. The energy expression is discretized by the differential quadrature finite element method, and furthermore the differential equation of the shaft-disk system is derived. In order to verify the convergence and calculation accuracy of the current model, a series of numerical examples are introduced. In addition, the influence of geometrical and material parameters on vibration results is discussed, while the boundary conditions and the cross-sectional shape of the disk are considered. It can be seen that the variation of the FGM parameters will affect the vibration characteristics within a certain range, while the frequency parameter with different disk cross-sectional shapes is different in sensitivity to parameter changes. The parametric analysis can provide reference for the determination of structure and material parameters.