考虑稳定性的非线性刚度转子系统振幅突变分叉集分析

中国机械工程

考虑稳定性的非线性刚度转子系统振幅突变分叉集分析

潘勇1;王香耿1;程敏2,3;刘保国2

1.河南机电职业学院机械工程学院，郑州,451191
2.河南工业大学机电工程学院，郑州，450001
3.中原工学院信息商务学院，郑州，450007

出版日期:2017-10-25 发布日期:2017-10-24
基金资助:
国家自然科学基金资助项目（11172092）；
河南省重点科技攻关项目（152102210366）；
河南省教育厅科学技术研究重点项目（14A460011）
National Natural Science Foundation of China （No. 11172092）

Analyses of Amplitude Catastrophe Bifurcation Sets for a Rotor System with Nonlinear Stiffness Considering Stability

PAN Yong1;WANG Xianggeng1;CHENG Min2,3; LIU Baoguo2

1.School of Mechanical Engineering,Henan Mechanical and Electrical Vocational College,Zhengzhou，451191
2.School of Mechanic & Electrical Engineering,Henan University of Technology,Zhengzhou，450001
3.College of Information & Business,Zhongyuan University of Technology,Zhengzhou，450007

Online:2017-10-25 Published:2017-10-24
Supported by:
National Natural Science Foundation of China （No. 11172092）

摘要/Abstract

摘要： 利用平均法导出非线性刚度转子系统的主共振频率响应方程，借助突变理论求出利用频率协调因子和激振力幅值表示的分叉集及其尖点表达式。根据奇点稳定性理论导出了转子系统稳定性条件，并得到利用频率协调因子和振幅构建的临界不稳定区域及其分叉点表达式。利用数值算例讨论了非线性刚度系数对分叉集突变区域、临界不稳定区域以及振幅特性曲线的影响。研究表明：减小转子系统的非线性刚度系数是控制转子系统振幅突变最为理想的方法。

关键词: 非线性刚度, 转子系统, 振幅突变, 分叉集

Abstract: With help of averaging method, a main resonance frequency response equation of a nonlinear stiffness rotor system was derived. Expressions of bifurcation set and its cusp were obtained based on catastrophe theory, which were represented by frequency coordination factor and excitation force amplitude. Stability conditions of a rotor system were derived based on stability theory of singular points, and expressions of critical unstable regions and its bifurcation points were also given by frequency coordination factor and amplitude. Influences of nonlinear stiffness on bifurcation catastrophe areas, unstable regions and amplitude characteristic curves were discussed though numerical examples. The results show that reducing nonlinear stiffness values is the best method to control amplitude catastrophe of the rotor systems.

Key words: nonlinear stiffness, rotor system, amplitude catastrophe, bifurcation set

中图分类号:

TH113.1
O192

潘勇1;王香耿1;程敏2,3;刘保国2. 考虑稳定性的非线性刚度转子系统振幅突变分叉集分析[J]. 中国机械工程.

PAN Yong1;WANG Xianggeng1;CHENG Min2,3; LIU Baoguo2. Analyses of Amplitude Catastrophe Bifurcation Sets for a Rotor System with Nonlinear Stiffness Considering Stability[J]. China Mechanical Engineering.

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