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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
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
  
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: 2607
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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