Longitudinal elastic wave propagation characteristics of inertant acoustic metamaterials

Abstract

Longitudinal elastic wave propagation characteristics of acoustic metamaterials with various inerter configurations are investigated using their representative one-dimensional discrete element lattice models. Inerters are dynamic mass-amplifying mechanical elements that are activated by a difference in acceleration across them. They have a small device mass but can provide a relatively large dynamic mass presence depending on accelerations in systems that employ them. The effect of introducing inerters both in local attachments and in the lattice was examined vis-à-vis the propagation characteristics of locally resonant acoustic metamaterials. A simple effective model based on mass, stiffness, or their combined equivalent was used to establish dispersion behavior and quantify attenuation within bandgaps. Depending on inerter configurations in local attachments or in the lattice, both up-shift and down-shift in the bandgap frequency range and their extent are shown to be possible while retaining static mass addition to the host structure to a minimum. Further, frequency-dependent negative and even extreme effective-stiffness regimes are encountered. The feasibility of employing tuned combinations of such mass-delimited inertant configurations to engineer acoustic metamaterials that act as high-pass filters without the use of grounded elements or even as complete longitudinal wave inhibitors is shown. Potential device implications and strategies for practical applications are also discussed.