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

万浩川;张琪昌;王炜

振动与冲击 ›› 2010, Vol. 29 ›› Issue (8) : 189-194.

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PDF(800 KB)
振动与冲击 ›› 2010, Vol. 29 ›› Issue (8) : 189-194.
论文

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

  • 万浩川1;张琪昌2;王炜2
作者信息 +

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

  • Wan Hao-chuan1;Zhang Qi-chang2;Wang Wei2
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文章历史 +

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( )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。

Abstract

The advanced conventional normal form method has only been used thus far in one or two dimensional systems and not yet in the study of multi-degree 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

Key words

complex normal form method / multi-degrees of freedom / strongly nonlinear oscillation / asymptotic solution

引用本文

导出引用
万浩川;张琪昌;王炜. 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[J]. 振动与冲击, 2010, 29(8): 189-194
Wan Hao-chuan;Zhang Qi-chang;Wang Wei. Application of complex normal form method in analysing strongly nonlinear vibration systems with three degrees of freedom[J]. Journal of Vibration and Shock, 2010, 29(8): 189-194

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