Energy Transport in 1-Dimensional Oscillator Arrays With Hysteretic Damping

TL;DR

This paper investigates energy transport in 1D oscillator chains with hysteretic damping, revealing how different hysteresis models affect supratransmission and wave spreading, with implications for engineering applications.

Contribution

It introduces and compares two models of hysteretic damping in oscillator chains, highlighting their effects on energy transmission phenomena.

Findings

Quantitative differences between the two hysteresis models in supratransmission behavior

Impact of hysteretic damping models on wave packet spreading

Differences observed in deterministic and stochastic settings

Abstract

Energy transport in 1-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 1-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.