轴向载荷作用旋转复合材料轴的动力学建模与参激失稳特性分析

doi:10.3901/JME.2025.07.396

机械工程学报 ›› 2025, Vol. 61 ›› Issue (7): 396-405.doi: 10.3901/JME.2025.07.396

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轴向载荷作用旋转复合材料轴的动力学建模与参激失稳特性分析

代其义¹, 韩勤锴², 秦朝烨², 褚福磊²

1. 北京工商大学机械工程系北京 100048;
2. 清华大学高端装备界面科学与技术全国重点实验室北京 100084

收稿日期:2024-04-24 修回日期:2024-10-16 发布日期:2025-05-12
作者简介:代其义，男，1989年出生，博士，副教授。主要研究方向为转子动力学、非线性振动、智能结构与主动控制。E-mail：daiqiyi1989@163.com
韩勤锴(通信作者)，男，1982年出生，博士，副研究员，博士研究生导师。主要研究方向为旋转机械动力学与故障诊断、能量收集利用、机械关键零部件寿命预测。E-mail：hanqinkai@mail.tsinghua.edu.cn<
基金资助:
国家自然科学基金资助项目(12102011，12272199)。

Dynamic Modeling and Parametric Instability Analysis of Rotating Composite Shafts Under Periodic Axial Loads

DAI Qiyi¹, HAN Qinkai², QIN Zhaoye², CHU Fulei²

1. Department of Mechanical Engineering, Beijing Technology and Business University, Beijing 100048;
2. State Key Laboratory of Tribology in Advanced Equipment, Tsinghua University, Beijing 100084

Received:2024-04-24 Revised:2024-10-16 Published:2025-05-12

摘要/Abstract

摘要： 建立了考虑材料内阻的旋转复合材料轴的动力学模型并分析了其在轴向周期载荷作用下的参激失稳特性。基于Bernoulli-Euler梁理论，采用Kelvin-Voigt模型描述复合材料的黏弹性阻尼耗散特性，建立了惯性系下旋转复合材料轴的运动微分方程。采用Galerkin法将偏微分方程组转化为具有周期时变系数的Mathieu-Hill型常微分方程组。基于对参激系统普遍适用的Floquet指数法对旋转复合材料轴受到轴向周期激励时的参激振动稳定性行为进行分析。通过与其他文献和数值积分结果的对比，验证了所建立模型及稳定性分析方法的正确性。在此基础上，研究了铺层角、内阻尼和静载荷系数等对旋转复合材料轴参激失稳区域大小和位置的影响。结果表明，由于转动效应的影响，旋转复合材料轴仅存在组合不稳定区，内阻尼对参激失稳特性具有显著的影响，增大铺层角、降低静载荷系数会使其参激振动稳定性增强。

关键词: 旋转复合材料轴, 轴向载荷, 参激失稳, 内阻尼, Floquet指数法

Abstract: The dynamic model of rotating composite shafts with internal damping is established and its parametric instability under periodic loads is studied. Based on Bernoulli-Euler beam theory and Kelvin-Voigt viscoelastic model, the governing equations of rotating composite shafts in inertial frame are derived. The partial differential equations are transformed into Mathieu-Hill ordinary differential equations with periodic coefficients using Galerkin method. Based on Floquet exponent method, which is widely used in parametric systems, the parametric stability behaviors of rotating composite shafts under axial periodic excitation are analyzed. The correctness of the model and the stability method is verified by comparing with other literatures and numerical integration results. On this basis, the effects of ply angle, internal damping and static load factor on the size and location of instability region of composite shafts are studied. The results show that due to the influence of rotation effect, only the combination instability region exists, and the internal damping has a significant influence on the parametric instability characteristics. Increasing the ply angle and decreasing the static load factor will improve the stability.

Key words: rotating composite shaft, axial loads, parametric instability, internal damping, Floquet exponent method

中图分类号:

TH113

代其义, 韩勤锴, 秦朝烨, 褚福磊. 轴向载荷作用旋转复合材料轴的动力学建模与参激失稳特性分析[J]. 机械工程学报, 2025, 61(7): 396-405.

DAI Qiyi, HAN Qinkai, QIN Zhaoye, CHU Fulei. Dynamic Modeling and Parametric Instability Analysis of Rotating Composite Shafts Under Periodic Axial Loads[J]. Journal of Mechanical Engineering, 2025, 61(7): 396-405.

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轴向载荷作用旋转复合材料轴的动力学建模与参激失稳特性分析

Dynamic Modeling and Parametric Instability Analysis of Rotating Composite Shafts Under Periodic Axial Loads

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