用改进平均法求解自由衰减振动

何松林;黄焱

振动与冲击 ›› 2011, Vol. 30 ›› Issue (1) : 227-229.

PDF(934 KB)
PDF(934 KB)
振动与冲击 ›› 2011, Vol. 30 ›› Issue (1) : 227-229.
论文

用改进平均法求解自由衰减振动

  • 何松林;黄焱
作者信息 +

The solution of the free damping vibration with improved averaging method

  • He Songlin; Huang Yan
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文章历史 +

摘要

为了提高平均法求解非线性振动的精度,必须考虑阻尼对振动周期影响,提出可将待解微分方程的圆频率与派生方程圆频率的差异函数表示为阻尼系数的多项式.通常只需取方程中一阶导数项的系数作为差异函数,就可在较大范围内提高平均法解的精度.利用改进平均法具体求解了线性阻尼衰减振动和杜芬型衰减振动,并与精确解或数值解进行了比较,证明改进平均法确实是有效的.



Abstract

In order to improve the accuracy of nonlinear vibration solution obtained by averaging method, the impact of damping on the vibration cycle must be considered.The different function of circular frequency, between the differential equation to be solved and the derived equation ,can be expressed as a polynomial of damping coefficient. Usually it will improve the accuracy of the averaging method in larger scale by take the damping coefficient as the different function easily.The linear damping vibration and Duffing-type damping vibration have been solved with improved averaging method .It is proved that the improved averaging method is effective to improve the accuracy of the solution by compare with the exact solution of the linear damping vibration and the numerical solution of the Duffing-type damping vibration.

关键词

非线性振动 / 阻尼系数 / 改进平均法

Key words

nonlinear vibration / damping coefficient / improved averaging method

引用本文

导出引用
何松林;黄焱. 用改进平均法求解自由衰减振动[J]. 振动与冲击, 2011, 30(1): 227-229
He Songlin;Huang Yan. The solution of the free damping vibration with improved averaging method[J]. Journal of Vibration and Shock, 2011, 30(1): 227-229

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