Publication: One-dimensional dispersion phenomena in terms of fractional media
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2016-09-19
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Springer
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Abstract
It 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.
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Couple stress theory, Continuum-mechanics, Nonlocal elasticity, Calculus, Derivatives, Models, Beams
Bibliographic citation
Sumelka, W., Zaera, R., & Fernández-Sáez, J. (2016). One-dimensional dispersion phenomena in terms of fractional media. European Physical Journal Plus, 131(9)