# Bound States in the Continuum in Elasticity

## TL;DR

This paper demonstrates the existence of bound states in the continuum (BSC) in elastic wave systems with two parallel arrays of subwavelength cylinders, supported by analytical solutions and interference effects.

## Contribution

It introduces the first analytical description of BSCs in elastic media with specific array configurations and identifies conditions for their existence.

## Key findings

- BSCs occur only at specific array distances and wave vectors.
- Analytic solutions for BSCs are derived.
- BSCs result from destructive interference of far-field resonances.

## Abstract

Diffraction of elastic waves is considered for a system consisting of two parallel arrays of thin (subwavelength) cylinders that are arranged periodically. The embedding media supports waves with all polarizations, one longitudinal and two transverse, having different dispersion relations. An interaction with scatters mixes longitudinal and one of the transverse modes. It is shown that the system supports bound states in the continuum (BSC) that have no specific polarization, that is, there are standing waves localized in the scattering structure whose wave numbers lies in the first open diffraction channels for both longitudinal and transverse modes. BSCs are shown to exists only for specific distances between the arrays and for specific values of the wave vector component along the array. An analytic solution is obtained for such BSCs. For distances between the parallel arrays much larger than the wavelength, BSCs is proved to exist due to destructive interference of the far field resonance radiation, similar to the interference in a Fabry-Perot interferometer, that can occur simultaneously for both propagating modes.