多频激励下达芬系统的超谐共振  

Super-harmonic resonance of Duffing-van der Pol system to multi-frequency excitation

作　　者：王利英[1] 赵卫国[1] 闫红艳[1] 田玉龙[2] 荀杰[1] 

机构地区：[1]河北工程大学水电学院,河北邯郸056021 [2]河北大学质量技术监督学院,河北保定071051

出　　处：《河北工程大学学报（自然科学版）》2007年第1期86-88,共3页Journal of Hebei University of Engineering:Natural Science Edition

摘　　要：达芬系统是自激系统的一个典型例子,研究多频激励下该系统的超谐共振在实际工程中很有现实意义。本文利用多尺度法研究了多频激励下达芬系统的超谐共振,得到了该系统的超谐共振的定常解,然后利用数值方法研究了系统参数对近似解幅频曲线的影响,并用数值仿真验证了结论的正确性。研究表明,超谐共振的幅频曲线具有叉型分岔的特性,此结果不仅可以用于分析类似系统的定常响应,而且为类似系统的设计和控制提供理论依据。Duffing-van der Pol system is the typical example of the self-excited system. It is important to study the super-harmonic resonances of the system in the engineering . In this paper the super-harmonic resonance of Duffing-van der Pol system is researched by the Multi-Scale Method, and the steady-state response is also obtained. Then the effects of all the parameters of the system on the amplitude-frequency curve are also discussed. Finally, the numerical method is used to verify the accordance. The results show pitchfork bifurcation arises in the turning point of amplitude-frequency curve. The results can not only be used to analyze the periodic solutions of similar system, but show theoretical foundation for design and control.

关 键 词：多尺度法 分岔 达芬系统 超谐共振 多频激励 

分 类 号：TH113.1[机械工程—机械设计及理论]