结构动力方程的一种自适应步长增维精细积分法  

Adaptive time-stepping increment-dimensional precise integration method for solving structural dynamic equations

作　　者：黄宇熙 崔颖 杨国刚[1] HUANG Yuxi;CUI Ying;YANG Guogang(Marin Engineering College,Dalian Maritime University,Dalian 116026,China;Naval Architecture and Ocean Engineering College,Dalian Maritime University,Dalian 116026,China)

机构地区：[1]大连海事大学轮机工程学院,辽宁大连116026 [2]大连海事大学船舶与海洋工程学院,辽宁大连116026

出　　处：《振动与冲击》2023年第14期198-203,236,共7页Journal of Vibration and Shock

基　　金：辽宁省自然科学基金指导计划(201602070)。

摘　　要：增维精细积分法是一种求解结构动力方程的高精度逐步积分算法,其步长的选取会对计算精度产生极大的影响,在实际应用中存在难以确定合适步长的问题。为满足实际工程中对计算精度和效率的要求,提出了一种计算误差的估计方法,并以估计误差和迭代收敛速度为基准,建立了一种自适应步长增维精细积分法。针对三种结构动力方程的算例结果表明,在计算各类线性及非线性振动问题时,该方法均可以在保证计算精度的前提下快速有效地控制算法的计算步长,并且仅需较少的额外计算消耗,显著提高了增维精细积分法的计算效率,使该方法在求解结构动力方程时更具计算优势和实用价值。The increment-dimensional precise integration method is a high-precision step-by-step integration algorithm for solving structural dynamic equations.The step size has a great influence on the calculation accuracy of the algorithm,and it is difficult to determine the appropriate step size in practical applications.To meet the requirements of accuracy and efficiency in the calculation,an estimation method for error calculation was proposed,and an adaptive time-stepping increment-dimensional precise integration method was established based on the estimation error and iterative convergence speed.The numerical results of three structural dynamic equations show that when considering all kinds of linear and nonlinear vibration problems,the proposed method can quickly and effectively control the calculation step size under the premise of ensuring the calculation accuracy,and only requires less additional calculation consumption,which significantly improves the efficiency of the increment-dimensional precise integration method,and offers more computational advantage and more practical value in solving structural dynamic equations.

关 键 词：增维精细积分法 步长自适应 结构动力方程 误差估计 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3