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Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(2): 187-191

Tao Ming-de. Asymptotic Solutions of Mathieu Equation with Damping[J]. Applied Mathematics and Mechanics, 1992, 13(2): 187-191.

Citation:

Tao Ming-de. Asymptotic Solutions of Mathieu Equation with Damping[J]. Applied Mathematics and Mechanics, 1992, 13(2): 187-191.

Tao Ming-de. Asymptotic Solutions of Mathieu Equation with Damping[J]. Applied Mathematics and Mechanics, 1992, 13(2): 187-191.

Citation:

Tao Ming-de. Asymptotic Solutions of Mathieu Equation with Damping[J]. Applied Mathematics and Mechanics, 1992, 13(2): 187-191.

Asymptotic Solutions of Mathieu Equation with Damping

Tao Ming-de

Department of Applied Mechanics, Fudan University, Shanghai

Received Date: 1989-12-16
Publish Date: 1992-02-15

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

References

[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).

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