Modulation Instability and Wavenumber Bandgap Breathers in a Time Layered Phononic Lattice

TL;DR

This paper reports the discovery of time-localized, spatially periodic breathers in a time-modulated phononic lattice, revealing new modulation instability conditions and experimental validation of these phenomena.

Contribution

It introduces the concept of wavenumber bandgap breathers in time-periodic phononic systems and derives exact conditions for their formation.

Findings

Wavenumber bandgap breathers are localized in time and periodic in space.

Modulation instability conditions lead to the formation of these breathers.

Experimental results qualitatively agree with the theoretical model.

Abstract

We demonstrate the existence of wavenumber bandgap (q-gap) breathers in a time-periodic phononic lattice. These breathers are localized in time and periodic in space, and are the counterparts to the classical breathers found in spatially-periodic systems. We derive an exact condition for modulation instability that leads to the opening of wavenumber bandgaps. The q-gap breathers become more narrow and larger in amplitude as the wavenumber goes further into the bandgap. In the presence of damping, these structures acquire a non-zero, oscillating tail. The experiment and model exhibit qualitative agreement.