Coupled free vibration of a functionally graded pre-twisted blade-shaft system reinforced with graphene nanoplatelets

The free vibration of a rotating functionally graded (FG) pre-twisted blade-shaft assembly reinforced with graphene nanoplatelets (GPLs) is analytically investigated based on the coupled model proposed in this paper. The effective material properties of the blade and shaft are assumed to vary continuously along their thickness and radius directions, respectively, and are determined by Halpin-Tsai micromechanics model and the rule of mixture. Within the framework of the Rayleigh beam theory and Euler-Bernoulli beam theory, the governing equations of motion are derived by using Lagrange's equation. The substructure synthesis method and assumed modes method are utilized to determine the natural frequencies of the system. A comprehensive parametric study is conducted to examine the effects of GPL weight fraction, distribution pattern, geometry and dimensions as well as the blade length, location and pre-twist angle, the shaft length and rotating speed on the natural frequencies. The research findings shed an important light on the design of novel graphene reinforced blade-shaft system for remarkably improved dynamic performance.