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

作　　者：王永 马骏 李靖翔 陈汝斯 许杨 郝跃东 胡鹏 WANG Yong;MA Jun;LI Jing-xiang;CHEN Ru-si;XU Yang;HAO Yue-dong;HU Peng(UHV Converter Station Branch of State Grid Shanghai Municipal Electric Power Company,Shanghai 201413,China;State Grid Hubei Electric Power Co.Ltd. ,Wuhan 430070,China;Guangzhou Bureau,CSG EHV Power Transmission Company,Guangzhou 510000,China;State Grid Hubei Electric Power Research Institute,Wuhan 430070,China)

机构地区：[1]国网上海市电力公司特高压换流站分公司,上海201413 [2]国网湖北省电力有限公司,武汉430070 [3]南方电网超高压公司广州局,广州510000 [4]国网湖北省电力有限公司电力科学研究院,武汉430070

出　　处：《计算力学学报》2020年第2期212-217,共6页Chinese Journal of Computational Mechanics

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。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.eH t 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.

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 

分 类 号：O322[理学—一般力学与力学基础]