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Asymptotic solutions of mathieu equation with damping

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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.

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References

  1. Liu, Z.R. and G.H. Ding, The Phenomenon on collapsible tube displacement oscillation and its theoritecal analysis,Advances in Hydrodynamics,3, 2 (1988), 1–10. (in Chinese)

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  2. Hsieh, D.Y., On Mathieu equation with damping,J. Math. Phys.,21 (1980), 722–725.

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  3. Nayfeh, A.H.,Perturbation Methods, John Wiley & Sons (1973).

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Authors and Affiliations

  1. Department of Applied Mechanics, Fudan University, Shanghai

    Tao Ming-de

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  1. Tao Ming-de
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Communicated by Dai Shi-qiang

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Ming-de, T. Asymptotic solutions of mathieu equation with damping. Appl Math Mech 13, 205–210 (1992). https://doi.org/10.1007/BF02454244

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  • DOI: https://doi.org/10.1007/BF02454244

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