| 一类含立方项非线性振动微分方程的解析解 |
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| 引用本文： | 何松林. 一类含立方项非线性振动微分方程的解析解[J]. 河南科技大学学报(自然科学版), 2011, 32(5): 85-88,1 |
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| 作者姓名： | 何松林 |
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| 作者单位： | 昆明学院物理科学与技术系,云南昆明,650214 |
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| 基金项目： | 云南省自然科学基金项目(2010ZC168); 云南省教育厅科学研究基金项目(2010Y503) |
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| 摘 要： | 依据弹性力作用下系统机械能守恒的原理,求解出一类含有线性项和立方项的非线性微分方程的雅克比椭圆函数型的精确解析解.通过对常见算例的讨论,以及与系统数值解的比较,说明了解析解是有效的.
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| 关 键 词： | 立方非线性 解析解 椭圆函数 |
Analytical Solution of Differential Equation of Nonlinear Vibration with Cubic Item |
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| HE Song-Lin. Analytical Solution of Differential Equation of Nonlinear Vibration with Cubic Item[J]. Journal of Henan University of Science & Technology:Natural Science, 2011, 32(5): 85-88,1 |
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| Authors: | HE Song-Lin |
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| Affiliation: | HE Song-Lin(Department of Physics Science & Technology,Kunming University,Kunming 650214,China) |
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| Abstract: | Based on the principle of mechanical energy conservation of the system under the action of elastic force,the accurate analytical solution of nonlinear vibration differential equation with a cubic term was obtained by elliptic function.With the discussion to common examples and comparing with the numberic results,it is found that the accurate analytical solution is valid within a wide range. |
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| Keywords: | Cubic nonlinearity Analytical solution Elliptic function |
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