Tunable dissipation in elastic metamaterials via methodic reconfiguration of inertant mechanical networks

Elastic metamaterials have proposed transformative solutions to applications in structural mechanics owing to their unique capabilities in the domain of wave propagation and control. Notable among them are inertant metamaterials which augment their locally resonant mechanism with mechanical inerters, thereby expanding their dispersion profiles and versatility. In this work, we provide a comprehensive analysis of the different ways such profiles can be shaped via an informed reconfiguration of a hierarchical mechanical network comprising the inerter element. Through a series of examples, we demonstrate the pivotal roles played by the network components, architecture, as well as damping placement on the response, bandgap characteristics, and emergent dissipation. Using the finite element method, band structures are computed for locally resonant flexural beams with six inertant networks representative of the design spectrum, via a free wave propagation approach, i.e., waves that are not driven at a given frequency. Predictions of the infinite medium reveal that each configuration is associated with its own dissipative characteristics which are depicted using a set of unique wavenumber-free band structures directly relating Bloch damping ratios to oscillatory damped frequencies. We show that the implemented framework enables a direct comparison with the finite metamaterial counterparts via modal damping ratios obtained at discrete frequencies, providing a straightforward yet firm validation of the resultant behavior across the entire frequency spectrum. Depending on the frequency range of interest, the choice of the inertant network combined with appropriate damping deployment within the host structure or the resonating substructure can be tailored to instigate an efficient damped response which is best suited for a given application. The presented work provides a new perspective on elastic metamaterials with inertant networks, elucidating the interplay between prescribed damping and emergent dissipation and changing the current paradigm from one that merely looks at damping amount to a cost-effective, placement-based strategy which maximizes the aggregate dissipation corresponding to a given amount of damping material.