A Fractional Acoustic Wave Equation from Multiple Relaxation Loss and Conservation Laws

摘要

This work concerns causal acoustical wave equations which imply frequency powerlaw attenuation. A connection between the fve-parameter fractional Zener wave equation, which is derived from a fractional stress-strain relation plus conservations of mass and momentum, and the physically well established multiple relaxation framework is developed. It is shown that for a certain continuous distribution of relaxation mechanisms, the two descriptions are equal.