One-dimensional dispersion phenomena in terms of fractional media Articles uri icon

publication date

  • September 2016

issue

  • 9

volume

  • 131

international standard serial number (ISSN)

  • 2190-5444

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.

keywords

  • Couple stress theory; Continuum-mechanics; Nonlocal elasticity; Calculus; Derivatives; Models; Beams