Abstract

This paper presents an investigation on vibration characteristics of graphene nanoplatelet (GPL) reinforced disk-shaft rotor with eccentric mass resting on elastic supports. The shaft is made of common metal material while the disk is made of graphene nanoplatelet reinforced material. The weight fraction of graphene nanoplatelets (GPLs) is assumed to vary smoothly and continuously along the thickness direction of the disk, which leads to a functionally gradient (FG) structure. The effective properties of the disk are determined via the Halpin-Tsai micromechanics model and the rule of mixture. In accordance with the Timoshenko beam theory and Kirchhoff plate theory, the governing equations which take into account gyroscopic effect due to rotation are derived by using the Lagrange equation. The substructure modal synthesis method and the assumed modes method are utilized to obtain the natural frequencies, and the Runge-Kutta method is adopted to solve the forced vibration response of the rotor system, where the centrifugal force and gravity of an eccentric mass in the shaft are considered as generalized forces. The present analysis is validated through comparison with both experiment and finite element (FE) results. A detailed parametric study is conducted to examine the effects of the rotating speed, GPL weight fraction, GPL distribution pattern, length-to-thickness ratio and length-to-width ratio of GPLs, disk position, disk dimension, and support stiffness on vibration behaviors of the nanocomposite disk-shaft rotor system.

摘要

本文介绍了石墨烯纳米片 (GPL) 增强型盘轴转子的振动特性研究，该转子具有位于弹性支撑上的偏心质量。轴由普通金属材料制成，而圆盘由石墨烯纳米片增强材料制成。假设石墨烯纳米片（GPLs）的重量分数沿着圆盘的厚度方向平滑连续地变化，这导致了功能梯度（FG）结构。圆盘的有效特性是通过 Halpin-Tsai 微力学模型和混合规则确定的。根据Timoshenko梁理论和Kirchhoff板理论，利用拉格朗日方程导出了考虑了旋转引起的陀螺效应的控制方程。采用子结构模态合成法和假设模态法求解固有频率，采用龙格-库塔法求解转子系统的受迫振动响应，其中轴内偏心质量的离心力和重力被认为是广义的力量。本分析通过与实验和有限元 (FE) 结果的比较得到验证。进行了详细的参数研究，以检查转速、GPL 重量分数、GPL 分布模式、GPL 的长厚比和长宽比、磁盘位置、磁盘尺寸和支撑刚度对振动的影响纳米复合材料盘轴转子系统的行为。采用龙格-库塔法求解转子系统的受迫振动响应，将轴内偏心质量的离心力和重力视为广义力。本分析通过与实验和有限元 (FE) 结果的比较得到验证。进行了详细的参数研究，以检查转速、GPL 重量分数、GPL 分布模式、GPL 的长厚比和长宽比、磁盘位置、磁盘尺寸和支撑刚度对振动的影响纳米复合材料盘轴转子系统的行为。采用龙格-库塔法求解转子系统的受迫振动响应，将轴内偏心质量的离心力和重力视为广义力。本分析通过与实验和有限元 (FE) 结果的比较得到验证。进行了详细的参数研究，以检查转速、GPL 重量分数、GPL 分布模式、GPL 的长厚比和长宽比、磁盘位置、磁盘尺寸和支撑刚度对振动的影响纳米复合材料盘轴转子系统的行为。本分析通过与实验和有限元 (FE) 结果的比较得到验证。进行了详细的参数研究，以检查转速、GPL 重量分数、GPL 分布模式、GPL 的长厚比和长宽比、磁盘位置、磁盘尺寸和支撑刚度对振动的影响纳米复合材料盘轴转子系统的行为。本分析通过与实验和有限元 (FE) 结果的比较得到验证。进行了详细的参数研究，以检查转速、GPL 重量分数、GPL 分布模式、GPL 的长厚比和长宽比、磁盘位置、磁盘尺寸和支撑刚度对振动的影响纳米复合材料盘轴转子系统的行为。