THE MATHEMATICAL PRINCIPLES OF VIBRATION REDUCTOR

Applied Mathematics and Mechanics (English Edition) ›› 1986, Vol. 7 ›› Issue (4): 355-363.

THE MATHEMATICAL PRINCIPLES OF VIBRATION REDUCTOR

卢亭鹤, 金均, 杭永珍

收稿日期:1985-06-15 出版日期:1986-04-18 发布日期:1986-04-18

THE MATHEMATICAL PRINCIPLES OF VIBRATION REDUCTOR

Lu Ting-he, Jin Jun, Hang Yong-zhen

Shanghai Teachers University, Shanghai

Received:1985-06-15 Online:1986-04-18 Published:1986-04-18

摘要/Abstract

摘要： In engineering and technology, it is often demanded that self-oscillation.be eliminated . 50 that the equipment or machinery may not be damaged. In this paper, a mathematical model for reducing vibration is given by the following equations:x₁+φ(x₁)+k₁(x₁-x₂)=0,x₂+cx₁+k₂(x₂-x₁)=0 (*)We have discussed how to choose suitable parameters c₁, k₁, k₂ of equations (*), so as to make the zero solution to be of global stability. Several theorems on the global stability of the zero solution of equations (*)are also given.

关键词: bifurcation, chaos, large amplitude, nonlinear

Abstract: In engineering and technology, it is often demanded that self-oscillation.be eliminated . 50 that the equipment or machinery may not be damaged. In this paper, a mathematical model for reducing vibration is given by the following equations:x₁+φ(x₁)+k₁(x₁-x₂)=0,x₂+cx₁+k₂(x₂-x₁)=0 (*)We have discussed how to choose suitable parameters c₁, k₁, k₂ of equations (*), so as to make the zero solution to be of global stability. Several theorems on the global stability of the zero solution of equations (*)are also given.

Key words: bifurcation, chaos, large amplitude, nonlinear

卢亭鹤;金均;杭永珍. THE MATHEMATICAL PRINCIPLES OF VIBRATION REDUCTOR[J]. Applied Mathematics and Mechanics (English Edition), 1986, 7(4): 355-363.

Lu Ting-he;Jin Jun;Hang Yong-zhen. THE MATHEMATICAL PRINCIPLES OF VIBRATION REDUCTOR[J]. Applied Mathematics and Mechanics (English Edition), 1986, 7(4): 355-363.

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THE MATHEMATICAL PRINCIPLES OF VIBRATION REDUCTOR

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