非线性动力方程的一种改进精细积分单步方法

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (5) : 182-188.

论文

刘冬兵1，王永2，李博文3，奕仲飞4，张磊4，黎慧2

作者信息 +

An improved precise integration single-step method for nonlinear dynamic equations

LIU Dongbing1, WANG Yong2, LI Bowen3, YI Zhongfei4, ZHANG Lei4, LI Hui2

Author information +

文章历史 +

摘要

微分求积法和单步块方法都是单步多级数值方法，但是直接应用于求解非线性动力方程时的计算量比较巨大，为此文中提出了一种基于单步块方法的改进精细积分单步方法。结合精细积分法，该方法采用s级的单步块方法的第s个方程对Duhamel积分项进行数值积分。具体采用四阶Runge-Kutta法获得待求变量的预估值，并采用新四点积分公式计算Duhamel积分项。相对于现有的单步方法，本文提出的改进算法在数值精度和稳定性上更优。通过非线性动力方程的典型算例验证了本文算法的优势。

Abstract

Differential quadrature method and single-step block method are both single-step and multi-level numerical methods, but they have a huge amount of calculation when they are directly applied to solve nonlinear dynamic equations. Therefore, an improved precise integration single-step method based on single-step block method is proposed in this paper. Combined with the precise integration method, this method uses the s-th equation of single-step block method of s-stage to conduct numerical integration of Duhamel integral term. Specifically, the fourth-order Runge Kutta method is used to obtain the estimated values of the variables, and the Duhamel integral term is calculated by the new four-point integral formula. Compared with the previous single-step method, the improved algorithm proposed in this paper has better numerical accuracy and stability. The advantages of the proposed algorithm are verified by typical examples of nonlinear dynamic equations.

导出引用

刘冬兵1，王永2，李博文3，奕仲飞4，张磊4，黎慧2. 非线性动力方程的一种改进精细积分单步方法[J]. 振动与冲击, 2022, 41(5): 182-188

LIU Dongbing1, WANG Yong2, LI Bowen3, YI Zhongfei4, ZHANG Lei4, LI Hui2. An improved precise integration single-step method for nonlinear dynamic equations[J]. Journal of Vibration and Shock, 2022, 41(5): 182-188

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