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arXiv · 2310.06934

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

Christopher Chong·Brian Kim·Evelyn Wallace·Chiara Daraio
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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.

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Christopher Chong, Brian Kim, Evelyn Wallace, Chiara Daraio. 2023-10-10. Modulation Instability and Wavenumber Bandgap Breathers in a Time Layered Phononic Lattice. https://arxiv.org/abs/2310.06934

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