具有曲率和惯性非线性以及材料内阻的旋转复合材料轴的主共振

发布时间：2018-07-08 11:50

  本文选题：主共振 + 旋转复合材料轴　； 参考：《力学学报》2017年04期

【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.
[Abstract]:As a kind of typical rotor dynamic system, rotating composite shaft has a wide application prospect in advanced helicopter and automobile power drive system. It has important theoretical and practical value to study the nonlinear vibration characteristics of rotating composite shaft. However, at present, the study of nonlinear vibration of rotating shaft is limited to isotropic metal material axis, and the influence of material internal resistance is seldom considered. In this paper, the principal resonance of rotating nonlinear composite axis with internal resistance is studied. The nonlinear curvature and nonlinear inertia caused by the large deformation of the inextensible composite axis are nonlinear and the internal resistance of the material is derived from the viscoelasticity of the composite. The dynamic modeling takes into account the moment of inertia and gyro effect. Based on the extended Hamilton principle, the partial differential equations of bending and bending coupled nonlinear vibration of a rotating composite axis with eccentric excitation are derived. The partial differential equation is discretized into ordinary differential equation by Galerkin method. The perturbation analysis of ordinary differential equation is carried out by using multi-scale method, and the analytical expression of principal resonance response is derived. The influence of the above parameters on the steady state forced vibration response of rotating nonlinear composite shaft is studied by numerical analysis of internal resistance, external resistance, layer angle, aspect ratio, layering mode and eccentricity. It is found that the internal resistance coefficient increases with the increase of the lamination angle, and the influence of the internal resistance on the main resonance response is mainly reflected in the stability of the suppression amplitude and the frequency response. The main resonance response near the forward precession natural frequency has typical nonlinear characteristics of hard spring. The model presented in this paper can be used to describe the principal resonance characteristics of rotating composite axis and is an important extension of the nonlinear dynamic model of non-extensible rotating metal axis.
【作者单位】： 山东科技大学机械电子工程学院;
【基金】：国家自然科学基金资助项目(11272190,11672166)
【分类号】：TB33;TH113
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本文编号：2107335