Sumelka, WojciechZaera, RamónFernández-Sáez, José2023-01-172023-01-172016-09-19Sumelka, W., Zaera, R., & Fernández-Sáez, J. (2016). One-dimensional dispersion phenomena in terms of fractional media. European Physical Journal Plus, 131(9)2190-5444https://hdl.handle.net/10016/36282It is well know that structured solids present dispersive behaviour which cannot be captured by the classical continuum mechanics theories. A canonical problem in which this can be seen is the wave propagation in the Born-Von Karman lattice. In this paper the dispersive effects in a 1D structured solid is analysed using the Fractional Continuum Mechanics (FCM) approach previously proposed by Sumelka (2013). The formulation uses the Riesz-Caputo (RC) fractional derivative and introduces two phenomenological/material parameters: 1) the size of non-local surrounding l(f), which plays the role of the lattice spacing; and 2) the order of fractional continua a, which can be devised as a fitting parameter. The results obtained with this approach have been compared with the reference dispersion curve of Born-Von Karman lattice, and the capability of the fractional model to capture the size effects present in the dynamic behaviour of discrete systems has been proved.9eng© The Author(s) 2016. This article is published with open access at Springerlink.comThis article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Atribución 3.0 EspañaCouple stress theoryContinuum-mechanicsNonlocal elasticityCalculusDerivativesModelsBeamsresearch articleIngeniería MecánicaMaterialeshttps://doi.org/10.1140/epjp/i2016-16320-3open access199The European Physical Journal Plus131AR/0000018290