Coupled vibration analysis of a rotating pre-twist blade-hub assembly with a setting angle reinforced by graphene nanoplatelets

Abstract

Due to its light weight and great mechanical performance, the spinning blade-hub assembly are widely used in modern rotary machines, such as the aero-engine, gas turbine, and so on. This paper conducted theoretical modeling and vibration analysis of a functionally graded (FG) pre-twist blade-hub rotor structure with a setting angle reinforced by graphene nanoplatelets (GPLs), where the hub and blade are modeled by elastic cylindrical shell and plate, respectively. To improve the structural stiffness, the blade-hub (plate-cylindrical shell) assembly is prepared from graphene nanoplatelet (GPL) reinforcement and polymer matrix. Both uniform and nonuniform GPL distributions are considered in the plate and cylindrical shell, which leads to a FG assembly. Determined via the Halpin-Tsai model and the rule of the mixture, the effective material properties vary continuously along the thickness direction of the plate and cylindrical shell. According to the Kirchhoff plate theory and the Donnell shell theory, the coupled equations of motion of the FG rotating blade-hub assembly are derived by using the Lagrange's equation. Moreover, the component mode synthesis (CMS) and assumed mode method are applied to obtain the free vibration results of the blade-hub rotor. By employing the finite element method, the theoretical model and analysis is verified. Finally, special attention is given to the influence of the material parameters (GPL distribution pattern, GPL weight fraction, GPL length-to-thickness ratio and GPL length-to-width ratio) and structural parameters (blade pre-twist angle and blade setting angle) on the free vibration frequency of the composite blade-hub rotor system.