Wave propagation in cellular locally resonant metamaterials

Abstract

Locally resonant acoustic metamaterials have recently attracted a great interest due to their dynamic behaviour, characterized by a band gap at relatively low frequencies. This paper provides a numerical study, by means of finite element modal analyses, of the dynamic properties of 1D mass-inmass and 2D cellular locally resonant metamaterials. The 2D metamaterial is constituted by a cellular metallic lattice, filled by a soft light material with heavy inclusions or resonators. The influence of material parameters and cell geometry on the band gap width and frequency level are explored. In addition to the usual square lattice we also consider a hexagonal one, which proves to be more efficient for wave filtering.

Homogenization Approach and Bloch-Floquet Theory for Band-Gap Prediction in 2D Locally Resonant Metamaterials

“…Various examples of LRM have been reported in the literature, they can be constituted by a periodic structure, made of a single material, with local resonators within the unit cell [12], by three components (e.g. hard inclusions with a soft coating embedded in a hard matrix [16,15] or cellular materials filled by a foam with hard inclusions [10]) or by two materials, typically soft inclusions in hard matrix, as studied e.g. in [22,14].…”

Band Gaps in Metamaterial Plates: Asymptotic Homogenization and Bloch-Floquet Approaches

“…This effect is due to the local resonance of some portions of the metamaterial which can trap the energy and attenuate wave propagation. Typically, LRM have a periodic or quasi-periodic structure consisting of a single material with local resonators inside the unit cells [14]; two-components materials, as studied, e.g., in [11,19,26]; or three components materials [10,12,21,24].…”

Band-gap structure in two- and three-dimensional cellular locally resonant materials

“…Such a scheme has been adopted for the mitigation of blast and impact effect, with encouraging results: the Authors of [21] have shown the results of a parametric study on the basis of a mathematical model; a practical implementation of such a concept can be found in [22], that contains also an experimental validation. In the framework of impact absorbers for crash-worthiness of lightweight cars, Comi and Driemeier [23,24] have proposed the adoption of a LRM with a different scheme: a square lattice of aluminium cells, filled by a polymeric foam, with circular lead inclusions. In that case, the study was focused on materials having two-dimensional periodicity and composed of long extruded cells that can be effectively studied by means of plane models considering propagation of pure transverse waves and planar waves separately .…”

“…The purpose of this paper is twofold. Firstly, the attention is focussed on the LRM with 2D periodicity, proposed in [24]. Such a metamaterial is characterized by an innovative design and shows the interesting property of overlapping band-gap for in-plane and transverse waves.…”

“…The objective is to understand the effect of the out-of-plane dimension, with a broader perspective with respect to previous works [25]. To this purpose, considering the LRM with 2D periodicity proposed in [24], various 3D models with different out-of-plane extensions are analyzed. The 3D and 2D band structures are obtained by means of finite-element modal analysis.…”