摘要
应用多尺度法分析了 van der Pol系统受参数激励和多频强迫激励联合作用下的主参数 -组合共振 ,求得了稳态响应的分岔方程 ,应用奇异性理论进行分析 ,得到了系统稳态响应的转迁集和分岔图 ,并分析了原系统参数对普适开折参数的影响。研究表明 ,该系统的稳态响应为一叉型分岔 ,激励幅值 F1 ,F2 和阻尼 μ对普适开折参数的影响很大 ,通过调整 F1 ,F2 和 μ可以很方便地控制解的分岔特性。
This paper presents the investigation of principal parametric-combination resonance in a parametrically and multi-frequency excited van der Pol's oscillator. The bifurcation equation is derived by the method of multiple scales and the transition varieties, and the bifurcation diagrams are obtained by the singularity theory. In addition, the influence of system parameters on universal unfolding parameters is studied. It is concluded that the response of this system is a pitchfork bifurcation and the influence of excitation amplitude F 1, F 2 and damping μ is great. The property of the solutions can be easily controlled by adjusting F 1, F 2 and μ .
出处
《振动．测试与诊断》
EI
CSCD
2003年第3期188-191,共4页
Journal of Vibration,Measurement & Diagnosis
基金
国家自然科学基金资助项目 (编号 :10 172 0 6 0 )
河北省教育厅博士基金资助项目 (编号 :B2 0 0 12 12 )
