有阻尼Mathieu方程的渐近解

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Asymptotic Solutions of Mathieu Equation with Damping

摘要: 本文从可瘪管的运动方程导出有阻尼Mathieu方程,然后用渐近展开法精确到各阶精度求得了稳定界限.指出了用平均变分法所得结果的精度,同时也解释了在实验中观察到的某些现象.
- 可瘪管 /
- Mathieu方程 /
- 参数激振
Abstract: This paper first reduces the motion equation of a collapsible tube to the Mathieu equation with damping.Then the stability charts correcting the accuracy to each order are obtained with the method of asymptotic expansions.The accuracy of the results obtained with the average variational method is shown, And some phenomena observed in the experiment are also explained.
- collapsible tube /
- Mathieu equation /
- parametric excitation

[1]	柳兆荣、丁光宏,可瘪管的位移振荡现象及其理论分析.水动力学研究与进展.3(2)(1988),1-10.
[2]	Hsieh,D.Y.,On Mathieu equation with damping,J.Math.Phys.,21(1980),722-725.
[3]	Nayfeh,A.H.,Perturbation Methods,John Wiley & Sons(1973).