A Fractional Acoustic Wave Equation from Multiple Relaxation Loss and Conservation Laws
arXiv:1202.4251
Abstract
This work concerns causal acoustical wave equations which imply frequency power-law attenuation. A connection between the five-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.
5 pages, 2 figures. Pre-print paper. Presented at the 5th IFAC Symposium on Fractional Differentiation and Its Applications (FDA 2012), Hohai University, Nanjing, China, 14-17 May 2012