An energy-based computational method in the analysis of the transmission of energy in a chain of coupled oscillators

TL;DR

This paper investigates how damping influences energy transmission in a semi-infinite chain of coupled oscillators modeled by modified sine-Gordon equations, using a finite-difference scheme and bifurcation analysis.

Contribution

It introduces a stable finite-difference method and analyzes damping effects on nonlinear supratransmission in coupled oscillator chains.

Findings

Damping affects the critical amplitude for supratransmission.

Numerical bifurcation analysis reveals damping delays phonon quenching.

The method accurately models energy injection and transmission phenomena.

Abstract

In this paper we study the phenomenon of nonlinear supratransmission in a semi-infinite discrete chain of coupled oscillators described by modified sine-Gordon equations with constant external and internal damping, and subject to harmonic external driving at the end. We develop a consistent and conditionally stable finite-difference scheme in order to analyze the effect of damping in the amount of energy injected in the chain of oscillators; numerical bifurcation analyses to determine the dependence of the amplitude at which supratransmission first occurs with respect to the frequency of the driving oscillator are carried out in order to show the consequences of damping on harmonic phonon quenching and the delay of appearance of critical amplitude.