具有内阻的旋转复合材料轴的非线性自由振动与稳定性

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摘要研究具有内阻的旋转复合材料轴的非线性自由振动和稳定性。采用大振幅不可伸缩旋转梁的假定，对复合材料轴进行非线性建模, 模型引入非线性曲率和惯性的影响。根据复合材料的粘弹性耗散特性描述材料内阻。从复合材料本构关系、应变-位移关系基本方程出发，在导出动能、势能和内阻耗散能的基础上，基于扩展的Hamilton原理，建立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。为了预测旋转复合材料轴的稳定边界，对线性化方程进行特征值分析，给出了临界速度和失稳阈的表达式。采用四阶Runge-Kutta法对常微分方程组进行数值积分，获得位移时间响应图、相平面图和功率谱图，研究了铺层角、长径比和铺层方式对非线性振动响应和稳定性的影响。

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	任勇生
	张玉环
	时玉艳

关键词 ：自由振动, 稳定性, 旋转复合材料轴, 内阻, 非线性曲率和惯性

Abstract：Nonlinear free vibration and stability of an internally damped rotating composite shaft are investigated. The shaft is assumed to be an in-extensional rotating beam with nonlinear curvature and inertia. Internal damping is described by the dissipative behavior of composite. Based on the constitutive relations and the strain-displacement relations of composite, the strain energy, the virtual dissipative work and the kinetic energy of the shaft are obtained. The equations of motion governing the nonlinear bending-bending vibration of rotating composite shaft are derived using extended Hamilton principle. The partial differential equations of motion are reduced into ordinary differential equations by Galerkin’s method. In order to find the boundaries of stability, the linearized model of composite shaft is used in eigenvalue analysis. The critical rotating speeds and instability thresholds of composite shaft are given. The fourth-order Runge-Kutta method is used to integrate numerically the differential equations of motion. The displacement-time responses, phase plane curves and power spectra of the shaft are presented. The effects of ply angle, ratio of length over outer radius and stacking sequence on the nonlinear bending vibration responses of composite shaft are evaluated.

Key words： Free vibration motion stability rotating composite shaft internal damping nonlinear curvature and inertia

收稿日期: 2016-11-22 出版日期: 2017-12-28

引用本文:

任勇生，张玉环,时玉艳. 具有内阻的旋转复合材料轴的非线性自由振动与稳定性[J]. 振动与冲击, 2018, 37(1): 117-127.
Ren Yongsheng, Zhang Yuhuan,Shi Yuyan. Nonlinear free vibration and stability of rotating composite shaft with internal damping. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(1): 117-127.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2018/V37/I1/117

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