Dynamic homogenization of composite and locally resonant flexural systems

TL;DR

This paper develops a frequency-dependent homogenization method for flexural systems that accurately models wave dispersion and dynamic response, especially in locally resonant media, without detailed field calculations.

Contribution

A simple, efficient method to derive frequency-dependent homogenized parameters that match exact dispersion relations in periodic flexural systems, including locally resonant media.

Findings

Homogenized model accurately reproduces low-frequency transmission characteristics.

Model's accuracy declines at higher frequencies, sensitive to microscale details.

Better performance in locally resonant media across wider frequency ranges.

Abstract

Dynamic homogenization aims at describing the macroscopic characteristics of wave propagation in microstructured systems. Using a simple method, we derive frequency-dependent homogenized parameters that reproduce the exact dispersion relations of infinitely periodic flexural systems. Our scheme evades the need to calculate field variables at each point, yet capable of recovering them, if wanted. Through reflected energy analysis in scattering problems, we quantify the applicability of the homogenized approximation. We show that at low frequencies, our model replicates the transmission characteristics of semi-infinite and finite periodic media. We quantify the decline in the approximation as frequency increases, having certain characteristics sensitive to microscale details. We observe that the homogenized model captures the dynamic response of locally resonant media more accurately and across a wider range of frequencies than the dynamic response of media without local resonance.