Aim of this paper is the study of waves propagation in a fractional, non-local 1D elastic continuum. The non-local effects are modeled introducing long-range central body interactions applied to the centroids of the infinitesimal volume elements of the continuum. These non-local interactions are proportional to a proper attenuation function and to the relative displacements between non-adjacent elements. It is shown that, assuming a power-law attenuation function, the governing equation of the elastic waves in the unbounded domain, is ruled by a Marchaud-type fractional differential equation. Wave propagation in bounded domain instead involves only the integral part of the Marchaud fractional derivative. The dispersion of elastic waves, as well as waves propagation in unbounded and bounded domains are discussed in detail.

Cottone, G., Di Paola, M., Zingales, M. (2009). Elastic waves propagation in 1D fractional non-local continuum. PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES, 2009 [10.1016/j.physe.2009.09.006].

Elastic waves propagation in 1D fractional non-local continuum

COTTONE, Giulio;DI PAOLA, Mario;ZINGALES, Massimiliano
2009-01-01

Abstract

Aim of this paper is the study of waves propagation in a fractional, non-local 1D elastic continuum. The non-local effects are modeled introducing long-range central body interactions applied to the centroids of the infinitesimal volume elements of the continuum. These non-local interactions are proportional to a proper attenuation function and to the relative displacements between non-adjacent elements. It is shown that, assuming a power-law attenuation function, the governing equation of the elastic waves in the unbounded domain, is ruled by a Marchaud-type fractional differential equation. Wave propagation in bounded domain instead involves only the integral part of the Marchaud fractional derivative. The dispersion of elastic waves, as well as waves propagation in unbounded and bounded domains are discussed in detail.
2009
Cottone, G., Di Paola, M., Zingales, M. (2009). Elastic waves propagation in 1D fractional non-local continuum. PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES, 2009 [10.1016/j.physe.2009.09.006].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/41543
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