Symbolic computation of strongly nonlinear periodic, oscillations
Symbolic computation of strongly nonlinear periodic, oscillations
复制标题
强非线性周期性振荡的符号计算
DOI：
10.1016/j.jsc.2013.03.006
复制
发表时间：
2013-08-01
影响因子：
0.7
通讯作者：
Li, Z. B.
中科院分区：
文献类型：
--
作者：
Liu, Y. P.;Liao, S. J.;Li, Z. B.
基于吴消元法和同伦分析法，提出了一种计算高非线性周期振荡精确解析逼近的算法。针对中心环和极限环周期振荡系统，开发了Maple软件包，该软件包能自动提供频率、运动平均值和振幅的精确近似值。由于HAM对高度非线性问题是有效的，该软件包可用于寻找具有强非线性的非线性振动系统的精确近似解。对于具有物理参数的系统，它可以提供可能的参数约束条件。最后给出了几个算例，说明了算法和Maple软件包的有效性和实用性。该软件包可在线免费获得，它为科学家和工程师提供了一个易于使用的工具，以解决具有高非线性的动态系统的周期振荡的精确近似。(C)2013爱思唯尔有限公司版权所有。
Based on Wu's elimination method and homotopy analysis method (HAM), an algorithm is proposed to compute accurate analytic approximation of periodical oscillations with high nonlinearity. A Maple package is developed for periodically oscillating systems of center and limit cycle types, which delivers accurate approximations of frequency, mean of motion and amplitude of oscillation automatically. Since HAM is valid for highly nonlinear problems, the package can be used to find accurate approximate solutions of nonlinear oscillation systems with strong nonlinearity. For systems with physical parameters, it can provide possible constraint conditions on parameters. Several examples are given to illustrate the validity and effectiveness of the algorithm and the Maple package. This package is freely available online, which provides an easy-to-use tool for scientist and engineer to solve accurate approximations of periodic oscillations of dynamic systems with high nonlinearity. (C) 2013 Elsevier B.V. All rights reserved.