  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.
