基于Matlab的平均加速度法求解二自由度动力方程的误差分析  

Based on Matlab average acceleration method for solving two degrees of freedom dynamic equations error analysist

作　　者：赵艳青[1] 宋伟志[1] 房祥波[1] 赵玉河[1] 

机构地区：[1]长安大学汽车学院,陕西西安710064

出　　处：《汽车实用技术》2013年第6期68-70,共3页Automobile Applied Technology

摘　　要：Newmark算法是求解结构动力学问题的主要方法之一,其精确度取决于时间步长h和最短固有周期T的比值^(h/T_(min))[1],对于已知最短固有周期T的系统,其精确度只与时间步长h有关。当Newmark算法的积分参数gama为1/2、beta为1/4时被称为平均加速度法[2],本文主要分析了平均加速度法与simulink中runge—kutta45算法的相对误差及绝对误差,验证了平均加速度法在步长为0.001时,可以达到所做项目的精度要求,本项目要求精度为千分之三。Newmark algorithm is one of the main methods which can be used to solve structure dynamics problem,its accuracy depends on the ratio of the time step h and the shortest natural period T,if the shortest natural period T is known,then the accuracy depends on the time step h only.When integral parameters of newmark algorithm,gama and beta,get the value 1/2 and 1/4 respectively,the newmark algorithm is called average-acceleration method.In this paper,relative error and absolute error between average-acceleration method and Runge—Kutta45 method used by simulink are analyzed,the result demonstrates that when time step is not bigger than 0.001s,the accuracy of average-acceleration method can meet the requirements that the error should be less than 0.3 percent.

关 键 词：MATLAB 平均加速度法 Runge-kutta45法 误差分析 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]