Improved accuracy of He’s energy balance method for analysis of conservative nonlinear oscillator
Improved accuracy of He’s energy balance method for analysis of conservative nonlinear oscillator
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DOI：
10.1007/s00521-014-1576-2
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发表时间：
2014-09
影响因子：
6
通讯作者：
Y. Khan;A. Mirzabeigy
中科院分区：
文献类型：
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作者：
Y. Khan;A. Mirzabeigy
本文结合搭配法和Galerkin-Petrov法的特点，提高了He能量平衡法分析保守型非线性振子的精度。为了验证该方法的有效性，分别考虑了三次非线性Duffing振子、双井Duffing振子和挂在旋转支承上的摆的非线性振荡。结果表明，改进后的能量平衡法可以有效地减小简单能量平衡法的误差。结果表明，改进的能量平衡法比基于配置的二阶能量平衡法和基于伽辽金法的二阶能量平衡法具有更好的精度。改进的能量平衡法可成功地用于其它保守型非线性振子的精确解析解。
In this paper, the accuracy of He’s energy balance method for the analysis of conservative nonlinear oscillator is improved based on combining features of collocation method and Galerkin–Petrov method. In order to demonstrate the effectiveness of proposed method, Duffing oscillator with cubic nonlinearity, double-well Duffing oscillator, and nonlinear oscillation of pendulum attached to a rotating support are considered. Comparison of results with ones achieved utilizing other techniques shows improved energy balance method can very effectively reduce the error of simple energy balance method. Also, results show in large amplitude of oscillation, and improved energy balance method yields better accuracy rather than second-order energy balance method based on collocation and second-order energy balance method based on Galerkin method. Improved energy balance method can be successfully used for accurate analytical solution of other conservative nonlinear oscillator.