CHAOS IN THE SOFTENING DUFFING SYSTEM UNDER MULTI-FREQUENCY PERIODIC FORCES

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (12): 1421-1427.

CHAOS IN THE SOFTENING DUFFING SYSTEM UNDER MULTI-FREQUENCY PERIODIC FORCES

楼京俊, 何其伟, 朱石坚

Institute of Noise &:Vibration, Naval University of Engineering, Wuhan 430033, P. R. China

收稿日期:2002-12-30 修回日期:2004-05-31 出版日期:2004-12-18 发布日期:2004-12-18
通讯作者: ZHU Shi-jian, Professor, Master Corresponding author,(Tel:+86-27-83443991:Fax:+86-27-83443990:E-mail:zhushj@public.wh.hb.cn) E-mail:zhushj@public.wh.hb.cn

CHAOS IN THE SOFTENING DUFFING SYSTEM UNDER MULTI-FREQUENCY PERIODIC FORCES

LOU Jing-jun, HE Qi-wei, ZHU Shi-jian

Institute of Noise &:Vibration, Naval University of Engineering, Wuhan 430033, P. R. China

Received:2002-12-30 Revised:2004-05-31 Online:2004-12-18 Published:2004-12-18

摘要/Abstract

摘要： The chaotic dynamics of the softening-spring Duffing system with multi-frequency external periodic forces is studied. It is found that the mechanism for chaos is the transverse heteroclinic tori. The Poincar? map, the stable and the unstable manifolds of the system under two incommensurate periodic forces were set up on a two-dimensional torus. Utilizing a global perturbation technique of Melnikov the criterion for the transverse interaction of the stable and the unstable manifolds was given. The system under more but finite incommensurate periodic forces was also studied. The (Melnikov's) global perturbation technique was therefore generalized to higher dimensional systems. The region in parameter space where chaotic dynamics may occur was given. It was also demonstrated that increasing the number of forcing frequencies will increase the area in parameter space where chaotic behavior can occur.

Abstract: The chaotic dynamics of the softening-spring Duffing system with multi-frequency external periodic forces is studied. It is found that the mechanism for chaos is the transverse heteroclinic tori. The Poincar? map, the stable and the unstable manifolds of the system under two incommensurate periodic forces were set up on a two-dimensional torus. Utilizing a global perturbation technique of Melnikov the criterion for the transverse interaction of the stable and the unstable manifolds was given. The system under more but finite incommensurate periodic forces was also studied. The (Melnikov's) global perturbation technique was therefore generalized to higher dimensional systems. The region in parameter space where chaotic dynamics may occur was given. It was also demonstrated that increasing the number of forcing frequencies will increase the area in parameter space where chaotic behavior can occur.

中图分类号:

O322
34C35

楼京俊;何其伟;朱石坚. CHAOS IN THE SOFTENING DUFFING SYSTEM UNDER MULTI-FREQUENCY PERIODIC FORCES[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(12): 1421-1427.

LOU Jing-jun;HE Qi-wei;ZHU Shi-jian . CHAOS IN THE SOFTENING DUFFING SYSTEM UNDER MULTI-FREQUENCY PERIODIC FORCES[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(12): 1421-1427.

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CHAOS IN THE SOFTENING DUFFING SYSTEM UNDER MULTI-FREQUENCY PERIODIC FORCES

CHAOS IN THE SOFTENING DUFFING SYSTEM UNDER MULTI-FREQUENCY PERIODIC FORCES

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