Platonic crystal with low-frequency locally resonant snail structures. Wave trapping, transmission amplification and shielding

TL;DR

This paper introduces a novel platonic crystal with snail resonators that achieve low-frequency wave trapping, transmission amplification, and vibration shielding, with potential applications in wave control and vibration suppression.

Contribution

It presents a new microstructured plate design incorporating snail resonators, demonstrating unique dynamic effects and a method to suppress low-frequency vibrations.

Findings

Demonstrates wave trapping and localization in the proposed structure.

Shows transmission amplification between plates separated by a ligament.

Provides a design procedure for vibration suppression in elongated plates.

Abstract

We propose a new type of platonic crystal. The proposed microstructured plate includes snail resonators with low-frequency resonant vibrations. The particular dynamic effect of the resonators are highlighted by a comparative analysis of dispersion properties of homo- geneous and perforated plates. Analytical and numerical estimates of classes of standing waves are given and the analysis on a macrocell shows the possibility to obtain localization, wave trapping and edge waves. Applications include transmission amplification within two plates separated by a small ligament. Finally we proposed a design procedure to suppress low frequency flexural vibration in an elongated plate implementing a by-pass system re- routing waves within the mechanical system.