Free vibration analysis of a functionally graded graphene nanoplatelet reinforced disk-shaft assembly with whirl motion

Abstract

ABSTRACT Free vibration behaviors of a functionally graded (FG) disk-shaft rotor system reinforced with graphene nanoplatelet (GPL) resting on elastic supports are investigated in this paper. The material properties of the shaft and disk are assumed to vary along their radius and thickness directions, respectively, and are determined by Halpin-Tsai model and the rule of mixture. The equations of motion including the gyroscopic effect due to rotation are derived by employing the Lagrange equation method within the framework of Timoshenko beam theory for the shaft and Kirchhoff plate theory for the disk. Substructure modal synthesis method and Galerkin method are then utilized to obtain the natural frequencies. The present analysis is validated against experimental and finite element results, which shows excellent agreement. A comprehensive parametric study on the effects of the weight fraction, distribution pattern, length-to-thickness ratio and length-to-width ratio of graphene nanoplatelets, as well as the shaft length, elastic support stiffness and rotating speed on the free vibration results are conducted to identify the effective ways to achieve greatly improved vibrational performance of the rotating FG-GPL disk-shaft assembly.