复规范形理论在研究三自由度强非线性振动问题中的应用  

Application of complex normal form method in analysing strongly nonlinear vibration systems with three degrees of freedom

作　　者：万浩川[1] 张琪昌[2] 王炜[1,2] 

机构地区：[1]乐山职业技术学院,乐山614000 [2]天津大学机械学院,天津300702

出　　处：《振动与冲击》2010年第8期189-194,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(10872141)

摘　　要：规范形理论在研究非线性动力系统的稳定性和分岔方面发挥了非常重要的作用,近年来,随着国内外学者在这一领域的研究不断深入,规范形理论本身和它在动力系统中的应用都取得了长足的进步。目前经过改进的规范形方法只是研究了一个自由度和两个自由度系统,而对于多自由度系统(n3)还几乎没有涉及,与此同时大多数工程实际结构需简化为多自由度强非线性振动模型。本文将规范形理论应用到多自由度强非线性振动系统中,采用改进的规范形方法研究三自由度强非线性振动系统的稳态渐近解,通过对比数值解及原有规范形方法的所得结果,验证了改进的规范形理论在研究多自由度强非线性振动系统渐近解求解方面的有效性。The advanced conventional normal form method for solving nonlinear constant differential equations has only been used thus for in one or two dimensional systems and not yet in the study of multi-degrees of freedom systems.In the paper,the normal form theory was extented to multi-degrees of freedom systems.The stable asymptotic solutions and limit cycles of strongly nonlinear oscillation systems with three-degrees of freedom and uncoupled in linear parts were investigated.The results testify the validity of the refined theory,which coincide with the solutions of numerical integration better than those of the initial normal form approach.

关 键 词：复规范形 三自由度 强非线性振动 渐进解 

分 类 号：O322[理学—一般力学与力学基础]