Wave equations, dispersion relations, and van Hove singularities for applications of doublet mechanics to ultrasound propagation in bio- and nanomaterials.
A fundamental mathematical framework for applications of Doublet Mechanics to ultrasound propagation in a discrete material is introduced. A multiscale wave equation, dispersion relation for longitudinal waves, and shear waves are derived. The van Hove singularities and corresponding highest frequency limits for the Mth-order wave equations of longitudinal and shear waves are determined for a widely used microbundle structure. Doublet Mechanics is applied to soft tissue and low-density polyethylene. The experimental dispersion data for soft tissue and low-density polyethylene are compared with results predicted by Doublet Mechanics and an attenuation model based on a Kramers-Kronig relation in classical continuum mechanics.
Wu
Junru
J
Department of Physics, University of Vermont, Burlington, Vermont 05405, USA. Jun-Ru.Wu@uvm.edu
Layman
Christopher
C
Liu
Jun
J
D003198:Computer Simulation; D004453:Echoencephalography / Q000706:statistics & numerical data; D004548:Elasticity; D006801:Humans; D019563:Mechanics; D008962:Models, Theoretical; D036103:Nanotechnology; D019047:Phantoms, Imaging; D020959:Polyethylene; D014463:Ultrasonography / Q000706:statistics & numerical data*
D020959:Polyethylene