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Electronic circuit equivalent of a mechanical impacting system

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Abstract

Mechanical impacting systems exhibit a large array of interesting dynamical behaviors including a large amplitude chaotic oscillation close to the grazing condition. This phenomenon has been explained by means of square-root singularity and the occurrence of dangerous border collision bifurcation. However, experimental investigation in the area is constrained by the fact that the parameters of such a mechanical system cannot be changed easily. Here, we propose an electronic circuit that can act as an analog of an impacting mechanical system. We show that the phenomena earlier reported through numerical simulation (like narrow-band chaos, finger-shaped attractor, etc.) occur in this system also. We have experimentally obtained the evolution of the chaotic attractor at grazing as the stiffness ratio is varied—which is not possible in mechanical experiments. We experimentally confirm the theoretical prediction that the occurrence of narrow-band chaos can be avoided for some parameter settings.

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Acknowledgements

SS acknowledges financial support from the Department of Science of Technology, Government of India, in the form of INSPIRE Fellowship, Reference No. IF150667. SB acknowledges financial support from the Science and Engineering Research Board, Department of Science and Technology, Government of India, in the form of J.C. Bose Fellowship, Project No. SB/S3/JCB-023/2015.

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  1. Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, India

    Soumyajit Seth & Soumitro Banerjee

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  1. Soumyajit Seth
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  2. Soumitro Banerjee
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Seth, S., Banerjee, S. Electronic circuit equivalent of a mechanical impacting system. Nonlinear Dyn 99, 3113–3121 (2020). https://doi.org/10.1007/s11071-019-05457-w

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