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结构动力学方程的辛RK方法

郭静 邢誉峰

郭静, 邢誉峰. 结构动力学方程的辛RK方法[J]. 应用数学和力学, 2014, 35(1): 12-21. doi: 10.3879/j.issn.1000-0887.2014.01.002
引用本文: 郭静, 邢誉峰. 结构动力学方程的辛RK方法[J]. 应用数学和力学, 2014, 35(1): 12-21. doi: 10.3879/j.issn.1000-0887.2014.01.002
GUO Jing, XING Yu-feng. Symplectic Runge-Kutta Method for Structural Dynamics[J]. Applied Mathematics and Mechanics, 2014, 35(1): 12-21. doi: 10.3879/j.issn.1000-0887.2014.01.002
Citation: GUO Jing, XING Yu-feng. Symplectic Runge-Kutta Method for Structural Dynamics[J]. Applied Mathematics and Mechanics, 2014, 35(1): 12-21. doi: 10.3879/j.issn.1000-0887.2014.01.002

结构动力学方程的辛RK方法

doi: 10.3879/j.issn.1000-0887.2014.01.002
基金项目: 国家自然科学基金(11172046;11172028;11372021)
详细信息
    作者简介:

    郭静(1983—),女,石家庄人,工程师,博士(通讯作者. Tel: +86-10-68384847; E-mail: guojing2662632@126.com

  • 中图分类号: O342;TU311.3

Symplectic Runge-Kutta Method for Structural Dynamics

Funds: The National Natural Science Foundation of China(11172046;11172028;11372021)
  • 摘要: 针对有阻尼和外载荷的线性动力学常微分方程,给出了s级2s阶隐式Gauss-Legendre辛RK(Gauss-Legendre symplectic Runge-Kutta, GLSRK)方法的一种显式高效的执行格式,首次给出了Gauss-Legendre辛RK方法和经典RK方法(classical RK, CRK)的谱半径和单步相位误差的显式表达式,并将两者进行了比较.线性多自由度系统和非线性Rayleigh系统数值算例表明,对结构动力学系统而言,辛RK方法远比经典RK方法优越,在运动学特性和长时间数值模拟方面尤为明显.
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出版历程
  • 收稿日期:  2013-07-15
  • 修回日期:  2013-10-21
  • 刊出日期:  2014-01-15

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