Modulation instability and wavenumber bandgap breathers in a time layered phononic lattice

Abstract

We provide the first experimental realization of wavenumber bandgap (q-gap) breathers. Experiments are obtained in the setting of a time-periodic phononic lattice where the model and experiment exhibit good qualitative agreement. q-gap breathers are localized in time and periodic in space, and are the counterparts to the classical breathers found in space-periodic systems. We derive an exact condition for modulation instability that leads to the opening of wavenumber bandgaps in which the q-gap breathers can arise. 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 nonzero, oscillating tail. The controllable temporal localization that q-gap breathers make possible has potential applications in the creation of phononic frequency combs, energy harvesting or acoustic signal processing.