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Asymptotic equivalence of homogenisation procedures and fine-tuning of continuum theories

This paper resulted from a collaboration between mathematics and engineering researchers. We present and demonstrate an approach that produces major improvements in the predictions of long-wave propagation in rods, when compared to the classic Rayleigh-Love model. This gives practitioners a model of wave dispersion behaviour which is simple, yet more accurate than other leading models. The work also provides an explanation for why the well-known Mindlin model of dynamic plate bending yields highly accurate results.