Newton方法在非线性振动理论中的推广与应用
Extension and Application of Newton’s Method in Nonlinear Oscillation Theory
-
摘要: 本文提出和证明了,用Newton方法可以求解强(弱)非线性非自治系统的渐近解析周期解,为研究强(弱)非线性系统振动提供了一个新的解析方法.根据本文方法的需要,讨论了二阶线性非齐次周期系统周期解的存在与计算问题.此外,还讨论了Newton方法对于拟线性系统的应用.最后,应用本文方法计算了Duffing方程的周期解.Abstract: In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for studying strong and weak nonlinear oscillation systems. On the strength of the need of our method, we discuss the existence and calculation of the periodic solution of the second order nonhomogeneous linear periodic system. Besides, we investigate the application of Newton's method to quasi-linear systems. The periodic solution of Duffing equation is calculated by means of our method.
-
Key words:
- Newton’s method /
- resonance /
- nonresonance /
- strongly nonlinear systems /
- truncated equations
-
[1] 李正元、钱敏,向量场的旋转度理论及其应用,北京大学出版社,北京(1982). [2] Боголюбов Н.Н.ц Ю.А.Митролъский,Асцмпмомцческце Мемобы Нелцнейных Колебанцй ИЗД 4-е,М,Наука(1974). [3] 马尔金,И,Г.《非线性振动理论中的李雅普诺夫与邦加来方法》,科学出版社,北京(1959). [4] Nayfeh and Mook,Nonlinear Oscillations,New york(1979). [5] 徐兆,非线性力学中的一种新的渐近方法,力学学报,17(3)(1985). [6] Li Li(李骊),The periodic solution of quasiconservative system,Proceedings of the Int,conf,on Nonl.,Mech,Science Press(1985). [7] Burton,T.D.,Nonlinear oscillation limit cycle analysis using a time transfor-mation approach,Int.J,Nonlinear Mech.,17(1)(]982). [8] Канторович Л.В.и Т.П,Акилов《泛函分析》,高等教育出版社,北京(1984). [9] 欧阳光中,《数学分析》,高等教育出版社(1985). [10] Канторович Л.В.и В.И.Соболев.Эпеменмы Функццоналъносо аналцза,Издатслъство Наука,Москва(1965). [11] 林千博,《物理系统中的非线性振动》,东北工学院理论力学教研室译(1980). -
点击查看大图
计量
- 文章访问数: 2171
- HTML全文浏览量: 73
- PDF下载量: 578
- 被引次数: 0
下载:
