| 王永,马骏,李靖翔,陈汝斯,许杨,郝跃东,胡鹏.非齐次动力学方程的一种精细积分单步方法[J].计算力学学报,2020,37(2):212~217 |
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| 非齐次动力学方程的一种精细积分单步方法 |
| A precise integration single-step method for nonhomogeneous dynamic equations |
| 投稿时间：2019-03-28 修订日期：2019-05-14 |
| DOI：10.7511/jslx20190328003 |
| 中文关键词: 非齐次动力学方程 精细积分法 微分求积法 变阶 单步法 |
| 英文关键词:nonhomogeneous dynamic equations precise integration method differential quadrature method variable order single-step method |
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| 摘要点击次数: 921 |
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| 中文摘要: |
| 针对非齐次动力学方程v=Hv+f（v，t），结合精细积分法和微分求积法，利用同阶的显式龙格-库塔法对计算过程中待求的vk+i/s（i=1，2，…，s）进行预估，提出了一种避免状态矩阵求逆的高效精细积分单步方法。该方法采用精细积分法计算eHt，而Duhamel积分项采用s级s阶的时域微分求积法，计算格式统一且易于编程，可灵活实现变阶变步长。仿真结果表明，与其他单步法及预估校正-辛时间子域法进行数值比较，该方法具有高精度、高效率及良好的稳定性，在求解大规模动力系统时间响应问题中具有较大的优势。 |
| 英文摘要: |
| Aiming at the nonhomogeneous equation v=Hv+f(v,t) used for a dynamic system,an efficient precise integration single-step method was proposed combined with the precise integration method (PIM) and the differential quadrature method (DQM).In the numerical integration process,the state matrix inversion was avoided and vk+i/s(i=1,2,…,s) is estimated by the explicit Runge-Kutta method in the same order with DQM. eHt is calculated by the PIM for the proposed algorithm,and the Duhamel integration term is calculated by the s-order s-order time-domain DQM.The algorithm is uniform and easy to be programmed,and the variable order and step-size can be flexibly realized.Compared with other single-step method and the predictor-corrector symplectic time-subdomain algorithm,the simulation results showed that the method has highly computational precision,high efficiency and good stability.It has great advantages in solving time response problems for large-scale dynamic systems. |
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