期刊
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
卷 16, 期 1, 页码 26-50出版社
WALTER DE GRUYTER GMBH
DOI: 10.2478/s13540-013-0003-1
关键词
fractional calculus; acoustical wave equations; elastic wave equations; fractional wave equations; fractional viscoelasticity; fractional ordinary and partial differential equations
资金
- Norwegian Research Council
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.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据