Road to Chaos for a Soft Spring System under Weak Periodic Disturbance

Liu Zeng-rong; Yao Wei-guo; Zhu Zhao-xuan

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Liu Zeng-rong, Yao Wei-guo, Zhu Zhao-xuan. Road to Chaos for a Soft Spring System under Weak Periodic Disturbance[J]. Applied Mathematics and Mechanics, 1986, 7(2): 103-108.

Citation:

Liu Zeng-rong, Yao Wei-guo, Zhu Zhao-xuan. Road to Chaos for a Soft Spring System under Weak Periodic Disturbance[J]. Applied Mathematics and Mechanics, 1986, 7(2): 103-108.

Citation:

Liu Zeng-rong, Yao Wei-guo, Zhu Zhao-xuan. Road to Chaos for a Soft Spring System under Weak Periodic Disturbance[J]. Applied Mathematics and Mechanics, 1986, 7(2): 103-108.

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Road to Chaos for a Soft Spring System under Weak Periodic Disturbance

1.
Anhui University, Hefei;
2.
Institute of Solid Physics, Beijing;
3.
Peking University, Beijing

Received Date: 1984-12-01
Publish Date: 1986-02-15

Abstract

Abstract

The Mel'nikov-Holmes method is used to discuss the road to chaos for an elastic system with soft spring constant and under weak periodic disturbance. It is found that according to how the disturbance is applied, forced vibration or parametric excitation, the response may pass to chaos through different sequences of subharmonic bifurcations, and that the orders in the sequences may be different for different disturbance frequencies.

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References(4)

References

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[2]	Morozov,A.D.,On the complete qualitative investigation of the equation of duffing,Differentialhiye Uravneniya,12(1976),241-255.
[3]	Hsieh,D.Y.,On Mathieu equation with damping,J.Math.Phys.,21(1980),722-725.
[4]	Gradshteyn,I.S.and I.M.Ryzhik,Table of Integrals,Series,and Products,Academic Press,8.11(1980).