Chaos in the Softening Duffing System Under Multi-Frequency Periodic Forces

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

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Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(12): 1299-1304

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, 2004, 25(12): 1299-1304.

Citation:

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, 2004, 25(12): 1299-1304.

Citation:

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, 2004, 25(12): 1299-1304.

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Chaos in the Softening Duffing System Under Multi-Frequency Periodic Forces

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

Received Date: 2002-12-30
Rev Recd Date: 2004-05-31
Publish Date: 2004-12-15

Abstract

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.
- multi-frequency excitation,
- softening Duffing system,
- chaos,
- heteroclinic torus

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References(20)

References

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