基于精细积分法的达芬方程分析  

Analysis of duffing equation based on precise integration

作　　者：赵真[1] 孙林[1] 任传波[1] 

机构地区：[1]山东理工大学交通与车辆工程学院,山东淄博255049

出　　处：《山东理工大学学报（自然科学版）》2009年第6期58-60,共3页Journal of Shandong University of Technology:Natural Science Edition

摘　　要：介绍了用精细积分求解动力学问题的方法,求解过程中将非线性项沿着系统以时间参数t按泰勒级数展开,结合Romberg积分法得到高精度的数值解.以此方法得到的计算结果为基准,做位移功率谱分析,绘制幅值改变时频率与振幅的关系曲线.通过求解达芬系统的自由振动方程证明了上述求解非线性动力学方程方法的有效性.The precise intergration method for solving nonlinear dynamics problems is intronduced in this paper.Following the system,the nonlinear term is treated with the Taylar＇s series expansion according to the time parameter during the solving process,and a high precision numerical solution is obtained with Romberg integration method.Based on the solution,the displacements were studied by power spectrum analysis and the curve of frequency-amplitude was plotted under different characteristic amplitude.Taking the free vibration of Duffing equation for example proves that this method is valid.

关 键 词：精细积分法 达芬系统的自由振动方程 泰勒级数 

分 类 号：N93[自然科学总论]