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On a fractional Zener elastic wave equation

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Abstract

This survey concerns a causal elastic wave equation which implies frequency power-law attenuation. The wave equation can be derived from a fractional Zener stress-strain relation plus linearized conservation of mass and momentum. A connection between this four-parameter fractional wave equation and a physically well established multiple relaxation acoustical wave equation is reviewed. The fractional Zener wave equation implies three distinct attenuation power-law regimes and a continuous distribution of compressibility contributions which also has power-law regimes. Furthermore it is underlined that these wave equation considerations are tightly connected to the representation of the fractional Zener stress-strain relation, which includes the spring-pot viscoelastic element, and by a Maxwell-Wiechert model of conventional springs and dashpots. A purpose of the paper is to make available recently published results on fractional calculus modeling in the field of acoustics and elastography, with special focus on medical applications.

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  1. Department of Informatics, University of Oslo, P.O. Box 1080, NO-0316, Oslo, Norway

    Sven Peter Näsholm & Sverre Holm

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Näsholm, S.P., Holm, S. On a fractional Zener elastic wave equation. fcaa 16, 26–50 (2013). https://doi.org/10.2478/s13540-013-0003-1

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