Abstract
The primary benefit of treating a complicated acoustic system as an acoustic metamaterial (AMM) is that once the effective material properties are determined, well-established mathematical analyses may be used to describe wave propagation within the system. However, many standard analyses are not well understood for the class of materials known as Willis materials. Willis materials are characterized by constitutive relations that couple both the pressure and momentum density to both the particle velocity and the volume strain. This work presents the mathematical analysis of the propagation of a velocity pulse of finite duration within a one-dimensional Willis material in the time-domain. In particular, the propagation of the pulse is described in the context of (i) an infinite Willis material, (ii) two half-spaces where one or both display Willis coupling, and (iii) a thin coupled partition in an uncoupled background. Willis coupling is shown to affect the relationship between incident and scattered waves via a convolution rather than a simple multiplication, as is the case with uncoupled media.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call