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Energy transport in one-dimensional oscillator arrays with hysteretic damping

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Abstract

Energy transport in one-dimensional oscillator arrays has been extensively studied to date in the conservative case, as well as under weak viscous damping. When driven at one end by a sinusoidal force, such arrays are known to exhibit the phenomenon of supratransmission, i.e. a sudden energy surge above a critical driving amplitude. In this paper, we study one-dimensional oscillator chains in the presence of hysteretic damping, and include nonlinear stiffness forces that are important for many materials at high energies. We first employ Reid’s model of local hysteretic damping, and then study a new model of nearest neighbor dependent hysteretic damping to compare their supratransmission and wave packet spreading properties in a deterministic as well as stochastic setting. The results have important quantitative differences, which should be helpful when comparing the merits of the two models in specific engineering applications.

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Acknowledgements

We are indebted to the referees for their very useful remarks, which helped us considerably improve our paper. TB acknowledges that the results of Sects. 2 and 5 were obtained under the scientific project no. 21-71-30011 of the Russian Science Foundation, and those of 3.1 and 3.2 under the Grant no. AP08856381 of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan, KazNU, Institute of Mathematics and Mathematical Modeling. CSp acknowledges partial support for this work by funds from the Ministry of Education and Science of Kazakhstan, in the context of the Nazarbayev University internal grant “Rapid response fixed astronomical telescope for gamma ray burst observation (RARE)” (OPCRP2020002).

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Authors and Affiliations

  1. Center for Integrable Systems, P.G. Demidov Yaroslavl State University, Yaroslavl, Russia

    Tassos Bountis

  2. Department of Mechanical and Aerospace Engineering, Nazarbayev University, Astana, Kazakhstan

    Konstantinos Kaloudis & Christos Spitas

  3. National University of Science and Technology “MISiS”, Moscow, Russia

    Joniald Shena

  4. Nonlinear Dynamics and Chaos Group, Department of Mathematics and Applied Mathematics, University of Cape Town, Cape Town, South Africa

    Charalampos Skokos

Authors
  1. Tassos Bountis
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  2. Konstantinos Kaloudis
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  3. Joniald Shena
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  4. Charalampos Skokos
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  5. Christos Spitas
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Corresponding author

Correspondence to Charalampos Skokos.

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Bountis, T., Kaloudis, K., Shena, J. et al. Energy transport in one-dimensional oscillator arrays with hysteretic damping. Eur. Phys. J. Spec. Top. 231, 225–236 (2022). https://doi.org/10.1140/epjs/s11734-021-00420-6

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