| 弹簧振子非线性振动的周期计算 |
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| 引用本文： | 林少光,龚善初.弹簧振子非线性振动的周期计算[J].湖南文理学院学报(自然科学版),2009,21(4):19-22. |
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| 作者姓名： | 林少光 龚善初 |
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| 作者单位： | 广东揭阳学院,机电工程系,广东,揭阳,522000 |
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| 基金项目： | 广东揭阳学院2006年院级重点科研资助项目 |
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| 摘 要： | 利用拉格朗日方程建立了弹簧振子非线性振动方程,应用第一类完全椭圆积分求出了非线性弹簧振子周期的精确解;应用迭代法求出了弹簧振子周期的近似解. 利用MAPLE 9.5计算机绘图,分别作出了周期精确解随振幅、弹簧原长、质量和劲度系数的变化曲线,并将Tex和Tapp进行了比较. 所得结论为周期与弹簧原长成正比,与振幅成反比;利用迭代法所求得的近似解与精确解比较,具较高的精度.
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| 关 键 词： | 弹簧振子 非线性振动 完全椭圆积分 迭代法 周期 精确解 近似解 |
Calculation of the nonlinear vibration Period of spring oscillator |
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| LIN Shao-guang,GONG Shan-chu.Calculation of the nonlinear vibration Period of spring oscillator[J].Journal of Hunan University of Arts and Science:Natural Science Edition,2009,21(4):19-22. |
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| Authors: | LIN Shao-guang GONG Shan-chu |
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| Institution: | LIN Shao-guang,GONG Shan-chu (Dept.of Mechanical & Elect.Engn.,Jieyang College,Jieyang,Guangdong,522000) |
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| Abstract: | By means of the Lagrange's equation,the nonlinear vibration equation of spring oscillator is established.Using the first kind of complete ellipse integral,the exact solution of the nonlinear spring oscillator period is got,and the curves of the exact solution of the period varying with amplitude,original spring length,spring mass and the coefficient of restoring force are drawn by using the MAPLE 9.5.The conclusions are that the period is in direct proportional to spring original length and in inverse propo... |
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| Keywords: | spring oscillator nonlinear vibration complete elliptic integral iterative method period exact solution approximate solution |
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