中文摘要：

旋转复合材料轴作为一类典型的转子动力学系统，在先进直升机和汽车动力驱动系统中有着广阔的应用前景.研究旋转复合材料轴的非线性振动特性具有重要的理论与实用价值.然而，目前有关旋转轴的非线性振动研究仅限于各向同性金属材料轴，很少考虑材料内阻的影响.本文研究具有材料内阻的旋转非线性复合材料轴的主共振.非线性来源于不可伸长复合材料轴的大变形引起的非线性曲率和非线性惯性，材料内阻来源于复合材料的黏弹性.动力学建模计入转动惯量和陀螺效应.基于扩展的Hamilton原理，导出具有偏心激励的旋转复合材料轴的弯--弯耦合非线性振动偏微分方程组.采用Galerkin法将偏微分方程离散化为常微分方程，采用多尺度法对常微分方程进行摄动分析，导出主共振响应的解析表达式.对内阻、外阻、铺层角、长径比、铺层方式和偏心距进行数值分析，研究上述参数对旋转非线性复合材料轴的稳态受迫振动响应行为的影响.研究发现，角铺设复合材料轴的内阻系数随着铺层角的增大而增大；内阻对主共振响应特性的影响主要体现在对抑制振幅和改变频率响应的稳定性方面；发生在正进动固有频率附近的主共振响应具有典型的硬弹簧非线性特性.本文提出的模型能够用于描述旋转复合材料轴的主共振特性，是对不可伸长旋转金属轴非线性动力学模型的重要推广.

英文摘要：

The rotating shaft made of anisotropic composites is a class of typical rotor dynamic system which has a wide application in the structural design of advanced helicopter power transmission and automotive drive system.The nonlinear rotordynamic behavior study of these system has significance in theory and practice.However,at present,the research about nonlinear dynamic of rotordynamic system has restrainedly been the rotating isotropic shaft,and the e_ect of internal material damping is seldom considered.In this paper,the primary resonances of an internally damped rotating composite shaft are investigated.Nonlinearity comes from curvature and inertia induced by large deformation of in-extensionality composite shaft.Internal material damping comes from the dissipative properties of viscoelastic composite.The dynamical model incorporates rotary inertia and gyroscopic e_ect.The extended Hamilton principle is employed to derive the nonlinear equations of bending-bending vibration of rotating composite shaft.The Galerkin method is used to discretize these nonlinear equations,and the multiscale method is adopted to perturbtion analysis the ordinary di_erential equation,then the analytical expression of primary resonances are derived.The internal damping,external damping,ply angle,length-diameter ratio,stacking sequence,and eccentic distance are numerically analyzed,the e_ects of above parameters on stable forced vibration-response behaviors of rotating nonlinear composite shaft are discussed.The results show that the internal damping coe_cient of angle-ply laminated shaft increases as the increase of ply angle.The primary resonance curves appeared at forward linear natural frequency are found to be of the hardening type.The developed model is capable of describing primary resonance behaviors of rotating composite shaft.This is an important generation of nonlinear dynamic model of in-extensional rotating isotropic shaft.