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摘要
This work presents a lossy partial differential acoustic wave equation including fractional derivative terms. It is derived from first principles of physics (mass and momentum conservation) and an equation of state given by the fractional Zener stress-strain constitutive relation. For a derivative order alpha in the fractional Zener relation, the resulting absorption alpha(k) obeys frequency power-laws as alpha(k) proportional to omega(1+alpha) in a low-frequency regime, ak alpha(k) proportional to omega(1-alpha/2) in an intermediate-frequency regime, and alpha(k) proportional to omega(1-alpha) in a high-frequency regime. The value alpha = 1 corresponds to the case of a single relaxation process. The wave equation is causal for all frequencies. In addition the sound speed does not diverge as the frequency approaches infinity. This is an improvement over a previously published wave equation building on the fractional Kelvin-Voigt constitutive relation.
- 出版日期2011-10
