Phase space analysis of nonlinear wave propagation in a bistable mechanical metamaterial with a defect

TL;DR

This paper investigates how solitary waves interact with defects in a bistable mechanical metamaterial, revealing complex behaviors like transmission, capture, and reflection influenced by energy exchange with localized breather modes.

Contribution

It introduces a reduced-order Hamiltonian model for wave-defect interactions and analyzes the phase space to understand the complex dynamics involved.

Findings

Wave interactions depend on initial speed and defect properties.

Energy exchange with breather modes governs wave behavior.

Phase space analysis uncovers the structure leading to different wave outcomes.

Abstract

We study the dynamics of solitary waves traveling in a one-dimensional chain of bistable elements in the presence of a local inhomogeneity (defect). Numerical simulations reveal that depending upon its initial speed, an incoming solitary wave can get transmitted, captured or reflected upon interaction with the defect. The dynamics are dominated by energy exchange between the wave and a breather mode localized at the defect. We derive a reduced-order two degree of freedom Hamiltonian model for wave-breather interaction, and analyze it using dynamical systems techniques. Lobe dynamics analysis reveals the fine structure of phase space that leads to the complicated dynamics in this system. This work is a step towards developing a rational approach to defect engineering for manipulating nonlinear waves in mechanical metamaterials.