ASYMPTOTIC SOLUTIONS OF MATHIEU EQUATION WITH DAMPING

Applied Mathematics and Mechanics (English Edition) ›› 1992, Vol. 13 ›› Issue (2): 205-210.

• 论文 • 上一篇

ASYMPTOTIC SOLUTIONS OF MATHIEU EQUATION WITH DAMPING

陶明德

Department of Applied Mechanics, Fudan University, Shanghai

收稿日期:1989-12-16 出版日期:1992-02-18 发布日期:1992-02-18

ASYMPTOTIC SOLUTIONS OF MATHIEU EQUATION WITH DAMPING

Tao Ming-de

Department of Applied Mechanics, Fudan University, Shanghai

Received:1989-12-16 Online:1992-02-18 Published:1992-02-18

摘要/Abstract

摘要： 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.

关键词: collapsible tube, mathieu equation, parametric excitation

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.

Key words: collapsible tube, mathieu equation, parametric excitation

陶明德. ASYMPTOTIC SOLUTIONS OF MATHIEU EQUATION WITH DAMPING[J]. Applied Mathematics and Mechanics (English Edition), 1992, 13(2): 205-210.

Tao Ming-de . ASYMPTOTIC SOLUTIONS OF MATHIEU EQUATION WITH DAMPING[J]. Applied Mathematics and Mechanics (English Edition), 1992, 13(2): 205-210.

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ASYMPTOTIC SOLUTIONS OF MATHIEU EQUATION WITH DAMPING

ASYMPTOTIC SOLUTIONS OF MATHIEU EQUATION WITH DAMPING

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