Enhanced inertia from lossy effective fluids using multi-scale sonic crystals

In this work, a recent theoretically predicted phenomenon of enhanced permittivity with electromagnetic waves using lossy materials is investigated for the analogous case of mass density and acoustic waves, which represents inertial enhancement. Starting from fundamental relationships for the homogenized quasi-static effective density of a fluid host with fluid inclusions, theoretical expressions are developed for the conditions on the real and imaginary parts of the constitutive fluids to have inertial enhancement, which are verified with numerical simulations. Realizable structures are designed to demonstrate this phenomenon using multi-scale sonic crystals, which are fabricated using a 3D printer and tested in an acoustic impedance tube, yielding good agreement with the theoretical predictions and demonstrating enhanced inertia.