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Review Article

A survey on fractional derivative modeling of power-law frequency-dependent viscous dissipative and scattering attenuation in acoustic wave propagation

[+] Author and Article Information
Wei Cai

College of Mechanical and Electrical Engineering, Hohai University, Changzhou 213022, China
cwprince@126.com

Wen Chen

State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 210098, China
chenwen@hhu.edu.cn

Jun Fang

State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 210098, China; Department of Informatics, University of Oslo, P. O. Box 1080, NO-0316 Oslo, Norway
346801730@qq.com

Sverre Holm

Department of Informatics, University of Oslo, P. O. Box 1080, NO-0316 Oslo, Norway
sverre@ifi.uio.no

1Corresponding author.

ASME doi:10.1115/1.4040402 History: Received December 15, 2017; Revised May 23, 2018

Abstract

This paper aims at presenting a survey of the fractional derivative acoustic wave equations, which have been developed in recent decades to describe the observed arbitrarily frequency-dependent attenuation and scattering of acoustic wave propagating through complex media. The derivation of these models and their underlying elasto-viscous constitutive relationships are reviewed, and the successful applications and numerical simulations are also highlighted. The different fractional derivative acoustic wave equations characterizing viscous dissipation are analyzed and compared with each other, along with the connections and differences between these models. These model equations are mainly classified into the two categories: the temporal and spatial fractional derivative models. The statistical interpretation for the range of power-law index is presented with the help of Lévy stable distribution. In addition, the fractional derivative biharmonic wave equations governing the scattering attenuation are introduced and can be viewed as a generalization of viscous dissipative attenuation models.

Copyright (c) 2018 by ASME
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