This paper presents a new theoretical model for rotating elastic hub-blade assemblies, made of functionally graded (FG) graphene nanoplatelet (GPL) reinforced nanocomposites, and their free vibration characteristics are investigated. This model is the first attempt to include two elastic components simultaneously and consider the coupled effect. The Euler-Bernoulli beam theory and the Donnell’s shell theory are employed to establish the mathematic model of the blade and hub, respectively. The effective material properties, varying continuously along the thickness of the beam and cylindrical shell, are determined via the Halpin-Tsai micromechanics model and the rule of the mixture. The Lagrange’s equation is adopted to derive the equations of motion which are then solved by employing the substructure mode synthesis method and the Galerkin method. A parametric study is conducted to examine the effects of the rotating speed, graphene nanoplatelet distribution pattern, GPL weight fraction, length-to-thickness ratio and length-to-width ratio of graphene nanoplatelets (GPLs) and blade dimension on the natural frequencies of the nanocomposite rotor system, which will significantly benefit on the structural and material design of GPL reinforced hub-blade assembly.

本文提出了一种由功能梯度（FG）石墨烯纳米片（GPL）增强纳米复合材料制成的旋转弹性轮毂叶片组件的新理论模型，并研究了其自由振动特性。该模型是首次尝试同时包含两个弹性组件并考虑耦合效应的尝试。分别采用欧拉-伯努利梁理论和唐内尔壳理论建立叶片和轮毂的数学模型。有效材料的性能沿着梁和圆柱壳的厚度连续变化，这取决于Halpin-Tsai微力学模型和混合物的规则。采用拉格朗日方程推导运动方程，然后通过子结构模式合成方法和伽勒金方法进行求解。