结构动力学方程的辛RK方法

郭静; 邢誉峰

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

郭静^1,2,
邢誉峰²

¹北京强度环境研究所可靠性与环境工程技术重点实验室, 北京 100076;²北京航空航天大学固体力学研究所, 北京100191

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
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- 文章访问数: 1173
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- 被引次数: 0
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

Symplectic Runge-Kutta Method for Structural Dynamics

GUO Jing^1,2,
XING Yu-feng²

¹Science and Technology on Reliability and Environment Engineering Laboratory, Beijing Institute of Structure and Environment Engineering, Beijing 100076, P.R.China;²The Solid Mechanics Research Center, Beihang University, Beijing 100191, P.R.China

Funds: The National Natural Science Foundation of China(11172046;11172028;11372021)

摘要

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.
- 辛 /
- RK方法 /
- 谱半径 /
- 人工阻尼 /
- 相位误差
Abstract: An explicit and efficient implementation of the symplectic implicit Gauss-Legendre Runge-Kutta (RK) method of stage s and order 2s,was presented for solution of the dynamical ordinary differential equation with physical damping and external loads. The analytical explicit spectral radii and single-step phase errors of the implicit Gauss-Legendre RK method were given and compared with those of the explicit classical RK method of stage 4 and order 4. Numerical comparisons through the dynamical solution of a linear multi-degree-of-freedom (MDOF) system and a nonlinear Rayleigh system were made to validate the present study and showed the advantages of the symplectic RK method over the classical RK method with numerical dissipation, especially in aspects of the kinematic properties and long time numerical simulation.
- symplectic /
- Runge-Kutta method /
- spectral radii /
- artificial damping /
- phase error

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参考文献(36)

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