| 非线性动力方程的改进分段直接积分法 |
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| 引用本文： | 王海波,余志武,陈伯望.非线性动力方程的改进分段直接积分法[J].工程力学,2008,25(9). |
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| 作者姓名： | 王海波 余志武 陈伯望 |
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| 作者单位： | 中南大学土木建筑学院，湖南城市学院土木工程学院 |
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| 基金项目： | 国家自然科学基金，湖南省教育厅科研项目 |
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| 摘 要： | 对现有的求解非线性动力方程v=H.v+f(v,t)的分段直接积分方法进行了改进,提出了新的预估式。该方法为显式预估-校正、自起步的单步四阶精度的精细积分算法,避免了对f(v,t)求导。算例表明:该文改进方法可用于求解多自由度、强非线性、非保守系统的动力响应问题;对研究解的稳定性也是一个有效的工具,而且比现有的分段直接积分方法和经典的Runge-Kutta方法计算精度高。
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| 关 键 词： | 非线性动力方程 分段直接积分法 精细积分法 预估-校正 Runge-Kutta方法 |
IMPROVED SEGMENTED-DIRECT-INTEGRATION METHOD FOR NONLINEAR DYNAMIC EQUATIONS |
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| WANG Hai-bo,YU Zhi-wu,CHEN Bo-wang.IMPROVED SEGMENTED-DIRECT-INTEGRATION METHOD FOR NONLINEAR DYNAMIC EQUATIONS[J].Engineering Mechanics,2008,25(9). |
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| Authors: | WANG Hai-bo YU Zhi-wu CHEN Bo-wang |
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| Abstract: | The present segmented-direct-integration method is improved for nonlinear dynamic systems governed by the equation v = H ? v +f ( v , t), and new predict formulas are proposed. As a precise integration method with explicit, predict-correct, self-starting and four order accuracy, the improved method is not necessary to differentiate f ( v,t). Numerical examples show that the improved method is suitable for multi-degrees of freedom, strongly nonlinear and non-conservative dynamic systems, even effective in studying stability of solution. Moreover, the improved method has higher accuracy than the present segmented-direct-integration method as well as classical Runge-Kutta integration method. |
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| Keywords: | nonlinear dynamic equations segmented-direct-integration method precise integration method predict-correct Runge-Kutta integration method |
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