# Subwavelength phononic bandgap opening in bubbly media

## TL;DR

This paper demonstrates the existence of subwavelength phononic bandgaps in bubbly media through analytical and numerical methods, introducing a novel formula for bubble resonance frequencies.

## Contribution

It provides an original formula for Minnaert resonance frequencies of arbitrarily shaped bubbles, advancing understanding of phononic bandgap phenomena in bubbly media.

## Key findings

- Existence of subwavelength phononic bandgap in bubbly media
- New analytical formula for bubble resonance frequencies
- Numerical experiments confirming theoretical predictions

## Abstract

The aim of this paper is to show both analytically and numerically the existence of a subwavelength phononic bandgap in bubble phononic crystals. The key is an original formula for the quasi-periodic Minnaert resonance frequencies of an arbitrarily shaped bubble. The main findings in this paper are illustrated with a variety of numerical experiments.