| 裘春航,吕和祥.在哈密顿体系下分析非线性动力学问题[J].计算力学学报,2000,17(2):127~132169 |
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| 在哈密顿体系下分析非线性动力学问题 |
| Solving the problems of nonlinear dynamics based on Hamiltonian system |
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| DOI：10.7511/jslx20002025 |
| 中文关键词: 非线性振动 精细积分 哈密顿体系 非线性动力学 |
| 英文关键词:nonlinear vibration,precise integration,Hamiltonian system,limit cycle |
| 基金项目:国家自然科学基金!重大项目 ( 1 9990 51 0 ) |
| 裘春航 吕和祥 |
| 大连理工大学工程力学系,大连 |
| 摘要点击次数: 3799 |
| 全文下载次数: 9 |
| 中文摘要: |
| 首先将ｎ维未知向量ｑ的二阶非线性力系统Ｍｑ＋Ｇｑ＋Ｋｑ＝Ｆ（ｑ，ｑ，ｔ）转化为与其等价的２ｎ维未知向量ｖ的一阶微分方程ｖ＝Ｈｖ＋ｆ（ｖ，ｔ），其中非线性部分ｊｉ（ｖ，ｔ）＝０（ｉ＝１，．．．ｎ），ｆｉ（ｖ，ｔ）＝Ｆｉ－ｎ（ｑ，ｑ，ｔ）（ｉ＝ｎ＋１，．．．２ｎ）；然后给出一种求解ｖ的逐步积分公式，从而将精细积分法进一步推广应用到非线性动力学问题。算例表明本方法的计算量较小且结果合理可靠。 |
| 英文摘要: |
| The second nonlinear system to be solved derived to the Hamitonian formulation dv/dt=Hv f(v,t), in which v is an unknown 2n\|dimensional vector, H is a coefficient matrix, and f(v,t) is its nonlinear part. Based on 2\ N type algorithm [3] , a precise time integration method with remarkable accuracy for solving such a nonlinear system is presented in this paper. The algorithm was proved highly effective for a series of numerical examples. |
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