Dynamic homogenization of composite and locally resonant flexural systems

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.