6533b828fe1ef96bd128907d
RESEARCH PRODUCT
Elastic waves propagation in 1D fractional non-local continuum
Massimiliano ZingalesGiulio CottoneMario Di Paolasubject
PhysicsNon-local elasticityContinuum mechanicsWave propagationDifferential equationMathematical analysisCondensed Matter PhysicsFractional calculuDispersion of elastic waves; Lattice models; Long-range interactions; Non-local elasticity; Fractional calculus; Fractional power lawPower lawAtomic and Molecular Physics and OpticsElectronic Optical and Magnetic MaterialsFractional calculusLattice modelLove waveLong-range interactionIngenieurwissenschaftenDispersion of elastic waveBounded functionddc:620Settore ICAR/08 - Scienza Delle CostruzioniLongitudinal waveFractional power lawdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-11-30 |