https://doi.org/10.1140/epjs/s11734-021-00420-6
Regular Article
Energy transport in one-dimensional oscillator arrays with hysteretic damping
1
Center for Integrable Systems, P.G. Demidov Yaroslavl State University, Yaroslavl, Russia
2
Department of Mechanical and Aerospace Engineering, Nazarbayev University, Astana, Kazakhstan
3
National University of Science and Technology “MISiS”, Moscow, Russia
4
Nonlinear Dynamics and Chaos Group, Department of Mathematics and Applied Mathematics, University of Cape Town, Cape Town, South Africa
Received:
7
September
2021
Accepted:
16
December
2021
Published online:
3
January
2022
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.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2022
