Extraordinary wave manipulation characteristics of nonlinear inertant acoustic metamaterials

Since being postulated more than a decade ago, inerters have been successfully employed to enhance the dynamic performance of mechanical systems in several applications. Their ability to lend a high dynamic mass presence to systems that employ them with only a relatively small static device mass makes them unique among mechanical elements. This study explores the mechanical wave manipulation characteristics of nonlinear inertant acoustic metamaterial (NLIAM) configurations using analysis and simulations for their one-dimensional discrete element lattice representations. Firstly, based on notional concepts for nonlinear inertant devices, potential frequency-dependent and acceleration-dependent nonlinear inertant models are identified. Using an effective mass model for the NLIAM with frequency-dependent inertance in the local resonator attachment, the dispersion characteristics of inverse square law and power law inertance models are examined and contrasted with those for an acoustic metamaterial with frequency invariant inertance. While a tuned inverse square law inertance model ensures the existence of a band gap over almost the entire frequency bandwidth of interest even encompassing the extremely low frequency regime, the low and high frequency limits for this inertance law would not be realizable in practice. A potentially more practical power law approximation is proposed and shown to deliver a widening of the band gap by more than 100% towards frequencies below the lower bound of the band gap for the acoustic metamaterial with frequency invariant inertance. Further, drawing inspiration from the Duffing-type stiffness, an acceleration-dependent cubically nonlinear inertance model is proposed. First order corrections to the dispersion characteristics are obtained for an NLIAM with acceleration-dependent inertance using a perturbation approach. For weakly nonlinear cases, excitation amplitude-activated shifts in the dispersion curves are found to enable this NLIAM to act as a passive adaptive filter for mechanical waves based solely on their excitation amplitude. Practical manifestations of such NLIAM could therefore provide a means to realize extraordinary wave manipulation capabilities especially suitable for low frequency structural dynamic applications. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.