ERRORS IN NUMERICAL SOLUTION OF EQUATION OF MOTION OF LIGHTLY DAMPED SDOF SYSTEM NEAR RESONANCE
ERRORS IN NUMERICAL SOLUTION OF EQUATION OF MOTION OF LIGHTLY DAMPED SDOF SYSTEM NEAR RESONANCE
复制标题
近共振小阻尼单自由度系统运动方程数值解的误差
DOI：
10.1142/s0219455405001477
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发表时间：
2005
影响因子：
3.6
通讯作者：
P. Reynolds
中科院分区：
文献类型：
--
作者：
A. Pavic;S. Z̆ivanović;P. Reynolds
本研究探讨当数值积分单自由度系统的运动方程时所产生的误差，该系统受共振附近的简谐力激励。由于常平均加速度法在许多有限元软件包中都有其特点，因此本文特别考虑了常平均加速度法。结果发现，由于众所周知的周期延长现象，在低阻尼系统的计算响应中出现相当大的误差。然而，对于具有较高阻尼的系统和/或当使用较小的时间步长时，误差减小。关于这一点，就获得具有预定准确度的解决方案所需的时间步骤提出了建议。
This study investigates the error which occurs when numerically integrating the equation of motion of a single degree of freedom system excited by a harmonic force near resonance. The Constant Average Acceleration method was considered in particular as it features in many finite element software packages. It was found that a considerable error in the calculated responses occurs in systems with low damping due to the well known phenomenon of period elongation. However, the error is reduced for systems with higher damping and/or when smaller time step is used. With regard to this, recommendations are given as to the time steps required to obtain solutions with a pre-defined level of accuracy.