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两自由度非对称三次系统非奇异时的非线性模态及叠加性*

徐鉴 陆启韶 黄克累

徐鉴, 陆启韶, 黄克累. 两自由度非对称三次系统非奇异时的非线性模态及叠加性*[J]. 应用数学和力学, 1998, 19(12): 1077-1086.
引用本文: 徐鉴, 陆启韶, 黄克累. 两自由度非对称三次系统非奇异时的非线性模态及叠加性*[J]. 应用数学和力学, 1998, 19(12): 1077-1086.
Xu Jian, Lu Qishao, Huang Kelei. Nonlinear Normal Modes and Their Superposition in a Two Degrees of Freedom Asymmetric System with Cubic Nonlinearities[J]. Applied Mathematics and Mechanics, 1998, 19(12): 1077-1086.
Citation: Xu Jian, Lu Qishao, Huang Kelei. Nonlinear Normal Modes and Their Superposition in a Two Degrees of Freedom Asymmetric System with Cubic Nonlinearities[J]. Applied Mathematics and Mechanics, 1998, 19(12): 1077-1086.

两自由度非对称三次系统非奇异时的非线性模态及叠加性*

基金项目: 国家自然科学基金(19602003);中国博士后基金
详细信息
  • 中图分类号: O322;TU311

Nonlinear Normal Modes and Their Superposition in a Two Degrees of Freedom Asymmetric System with Cubic Nonlinearities

  • 摘要: 本文利用非线性模态子空间的不变性研究两自由度非对称三次系统在非奇异条件下的非线性模态及其模态叠加解有效性,重点考虑这种有效性与模态动力学方程静态分岔之间的关系.大量的数值结果表明,非线性模态解的有效性不仅与其局部性的限制有关,而且与模态动力学方程静态解分岔有关.
  • [1] R.M.Rosenberg,Normal modes in nonlinear dual-mode systems,J.Appl.Mech.,27(3)(1960),263-268.
    [2] R.M.Rosenberg,On normal vibrations of a general class of nonlinear dual-mode systems,J.Appl.M ech.,28(3)(1961),275-283.
    [3] R.M.Rosenberg,The normal modes of nonlinear n-degree of freedom systems,J.Appl.Mech.,30(1)(1962),7-14.
    [4] R.M.Rosenberg,On a geometrical method in nonlinear vibrations,in Les Vibrations Forces dans systems Non linearies,Int.Conf.in Nonlinear Vibrations,Marseille(1964).
    [5] R.M.Rossenberg,On nonlinear vibrations of systems with many degrees of freedom,Adv.Appl.Mech.,8(2)(1966),155-242.
    [6] S.W.Shaw and C.Pierre,Normal modes for nonlinear vibrations systems,J.Sound Vibration,164(1)(1993),35-122
    [7] G.V.Anand,Natural modes of a coupled nonlinear system,Internat.J.Non-Linear Mech.,7(1)(1972),81-91.
    [8] A.K.Mishra and M.C.Singh,The normal modes of nonlinear symmetric systems by group representation theory,Internat.J.Non-Linear.Mech.,9(4)(1974),463-480.
    [9] T.K.Caughey,A.Vakakis and J.M.Sivo,Analytical study of similar normal modes and their bifurcations in a class of strongly nonlinear systems,Internat.J.Non-Linear Mech.,25(5)(1990),521 533.
    [10] T.L.Jonson and R.Rand,On the existence and bifurcation of minimal modes,Internat.J.Non-Linear Mech.,14(1)(1979),1-12.
    [11] 陈予恕、徐鉴,Vandel Pol-Duffing-Mathieu型方程主参数共振分叉解的普适性分类,中国科学A辑,25(12)(1995),1281-1297.
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  • 被引次数: 0
出版历程
  • 收稿日期:  1996-09-02
  • 修回日期:  1997-03-20
  • 刊出日期:  1998-12-15

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