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轴向运动弦线非线性动力学和控制

批准号10172056 学科分类土壤化学 ( D070103 )
项目负责人董元华 负责人职称 依托单位上海大学
资助金额0.00
万元
项目类别面上项目 研究期限2002 年 01 月 01 日 至
2004 年 12 月 01 日
中文主题词轴向运动弦线;非线性参数振动;混沌;数值算法;守恒量
英文主题词axailly moving strings; nonlinear parametric vibration; chaos; numerical schemes; conserved quantities

摘要

中文摘要 应用和发展经典非线性振动、非线性动力学和分布参数系统控制理论,研究弹性和粘弹性轴向运动弦线的稳定性、分岔和混沌,考察Galerkin截断在动力学行为分析中的适用性,结合具体系统和工况设计控制律进行纵向振动的主动控制。本项目的研究成果将丰富和发展非线性系统的动力学和控制理论,为平带驱动装置等工程系统的设计及其控制提供理论储备。
英文摘要 An axially moving string is a simplest representative of gyroscopic continua. The approaches to analyze axially moving strings can be extended to other more complicated gyroscopic continua. An axially moving string also serves as the mechanical model of many engineering devices. The main contents of the project include: stead-state responses in nonlinear parametric vibration and their stability, bifurcation and chaos, numerical simulation schemes, energetics and conserved quantities, and control of transverse vibration. The main contributions are: new understanding of "the quasi-static stretch assumption" in modeling transverse nonlinear vibration, extension of the method of multiple scales to nonlinear partial-differential- integral equations in the case of nonlinear vibraiton of axially moving strings with an integral constitutive law, investigations on bifurcation and chaos in transvere motion of axially moving strings, development of some numerical schemes, and discovery of energetics and energy-like conserved quantities in nonlinear vibration of axially moving strings. Those controbutions proposed a new approach to model inevitabe damping factors in the engineering systems, sharpened the corresponding methods of modeling and analysis, presented a new interpretation of broad-band noise in the engineering systems, and laid foundations for stability analysis and control design. The group published 35 journal papers, including 23 papers appearing in international journals, among which, 25 paeprs were indexed by SCI, and 19 by EI. Some papers have been cited by peers. Especially, a reviewing paper was published in ASME Applied Mechanics Reviews, and an session lecture was presested in the 21th International Congress of Theoretical and Applied Mechanics.
结题摘要 轴向运动弦线是最基本的陀螺连续体,分析轴向运动弦线的方法可能推广到其它更复杂的陀螺连续体;轴向运动弦线也是多种工程装置的力学模型。本项目主要内容包括:非线性参数振动的稳态响应及其稳定性,分岔和混沌,数值仿真算法,能量关系和守恒量,横向振动的控制。主要成果包括:对横向非线性振动建模中的"准静态假设"提出新的认识,结合积分型本构粘弹性弦线的非线性振动分析将多尺度法推广到偏微分-积分方程,首次研究了轴向运动弦线横向振动中的分岔和混沌问题,发展了轴向运动弦线横向振动的通用数值仿真方法,首次导出了轴向运动弦线非线性振动中的能量关系并发现类能量守恒量。这些工作提出工程系统中必然存在的耗散因素模型化的新途径,发展了相应的建模和分析方法;为工程系统中的宽频噪声提出新的可能解释,为控制系统的稳定性分析和控制设计研究奠定基础。本课题组发表期刊论文35篇,其中国际期刊论文23篇,被SCI收录25篇,被EI收录19篇。相关论文已被国内外同行应用。长篇综述已在ASME Applied Mechanics Reviews发表。相关成果曾在第21届国际理论与应用力学大会上作20分钟分组报告。

成果

序号 标题 类型 作者
1 轴向运动弦线横向振动的频域分析. 期刊 刘芳|陈立群|
2 Energetics and conserved functional of moving materials undergoing transverse nonlinear vibration. 期刊 Li-Qun Chen|Jean W. Zu|
3 Transverse vibrations of an axially accelerating viscoelastic string with geometric nonlinearity. 期刊 Li-Qun Chen|Jean W. Zu|Jun Wu|Xiao-Dong Yang|
4 The chaotic response of the viscoelastic traveling string: an integral constitutive law. 期刊 Li-Qun Chen|Jun Wu|Jean W. Zu|
5 Principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string. 期刊 Liqun Chen|Jean W. Zu|Jun Wu|

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