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On Application Melnikov Method to Detecting the Edge of Chaos for a Micro-Cantilever

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New Advances in Mechanisms, Mechanical Transmissions and Robotics

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 46))

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Abstract

In this paper, Melnikov method is employed to detecting the edge of chaos for a micro-cantilever. The difficulties arising from the integrals in Melnikov method are refrained through using MATLAB/Simulink. The edge of chaos plotted on a two parameter plane indicate that the condition of chaos occurrence derived from Melnikov method is compact for some system parameters, but is conservative for the others. Therefore, applying Melnikov method to detecting edge of chaos is far from perfect method.

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Acknowledgments

The authors would like to acknowledge the financial support of NSFC (National Natural Science Foundation of China) under the grant No. 51175437 and No. 51575457.

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Authors and Affiliations

  1. School of Mechanical Engineering, Southwest Jiaotong University, Leshan, People’s Republic of China

    J. Xie, S.-H. He, Z.-H. Liu & Y. Chen

Authors
  1. J. Xie
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  2. S.-H. He
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  3. Z.-H. Liu
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  4. Y. Chen
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Corresponding author

Correspondence to J. Xie .

Editor information

Editors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Burkhard Corves

  2. University Politehnica of Timisoara , Timisoara, Romania

    Erwin-Christian Lovasz

  3. RWTH Aachen University Dept of Mechanism Theory, Aachen, Nordrhein-Westfalen, Germany

    Mathias Hüsing

  4. University Politehnica of Timisoara , Timisoara, Romania

    Inocentiu Maniu

  5. University Politehnica of Timisoara, Timisoara, Romania

    Corina Gruescu

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Xie, J., He, SH., Liu, ZH., Chen, Y. (2017). On Application Melnikov Method to Detecting the Edge of Chaos for a Micro-Cantilever. In: Corves, B., Lovasz, EC., Hüsing, M., Maniu, I., Gruescu, C. (eds) New Advances in Mechanisms, Mechanical Transmissions and Robotics. Mechanisms and Machine Science, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-319-45450-4_16

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  • DOI: https://doi.org/10.1007/978-3-319-45450-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45449-8

  • Online ISBN: 978-3-319-45450-4

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