指数时间差分法在旋转柔性梁动力学仿真中的应用策略  

Application strategy of exponential time differencing method in dynamic simulations of rotating flexible beams

作　　者：方思明 王贤明 郭书豪 FANG Siming;WANG Xianming;GUO Shuhao(College of Mechanical Engineering,Zhejiang University of Technology,Hangzhou 310014)

机构地区：[1]浙江工业大学机械工程学院,杭州310014

出　　处：《高技术通讯》2023年第9期990-999,共10页Chinese High Technology Letters

基　　金：国家自然科学基金(11602220)资助项目。

摘　　要：本文针对非惯性系下旋转柔性梁的数值仿真,研究指数时间差分法(ETD)的应用策略。作为一种指数积分法,ETD格式中指数积分项所涉及的矩阵指数(被称为线性算子)的合理选取对于旋转柔性梁动力学这类数值刚性问题的有效求解十分关键。考虑到旋转柔性梁动力刚化等物理特性,将系统大范围转动的信息纳入线性算子的构造。数值算例结果表明,线性算子的选取对算法的稳定性以及精度都有很大影响,根据角速度来选取线性算子是一种合理、有效的方式。对于本文的算例,当线性算子取为最大角速度时的Jacobian矩阵时,ETD格式求解的稳定性最好。总之,本文的线性算子选取策略可以提高ETD格式的数值稳定性和求解效率。This paper studies the application strategy of exponential time differencing(ETD)schemes for numerical simulations of rotating flexible beams in non-inertial systems.The matrix exponential involved in the exponential integral term is called linear operator in the exponential integrators.This work focuses on the selection of linear operators.The dynamic equations of rotating flexible beams usually are stiff,after being spatially discretized by numerical methods such as the finite element method.Regarding the dynamic characteristics of the rotating flexible beam,such as dynamic stiffening,the information of the system’s large-scale swing is taken consideration into the selection of the linear operator.Numerical testing results show that the linear operator is very important for the stability of ETD schemes used to solve stiff problems.We take the Jacobian matrix at the maximum angular velocity as the linear operator for the ETD schemes.This improves the stability and thus the total efficiency of ETD schemes.

关 键 词：旋转柔性梁 动力学数值仿真 刚性微分方程 指数时间差分法 线性算子 

分 类 号：O342[理学—固体力学] TP391.9[理学—力学]