2013/06/30 by Sverre Holm, Sven Peter Näsholm · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Attenuation #Constitutive equation #Damped wave #Fractional Differential Equations Solutions #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Structural Health Monitoring Techniques #Ultrasonics and Acoustic Wave Propagation #Wave equation #physics.class-ph
paper · pdf · doi:10.1016/j.ultrasmedbio.2013.09.033
Paper accepted for publication in Ultrasound in Medicine & Biology (Elsevier)
openalex publication_date 2014/01/14 · arxiv created 2014/01/27 · arxiv updated 2014/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A set of wave equations with fractional loss operators in time and space are analyzed. It is shown that the fractional Szabo equation, the power law wave equation, and the fractional Laplacian wave equation in the causal and non-causal forms all are low frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional constitutive equations while the former wave equations are ad hoc, heuristic equations. We show that this has consequences for use in modelling and simulation especially for applications that do not satisfy the low frequency approximation, such as shear wave elastography. In such applications the wave equations based on constitutive equations are the preferred ones.