Elastic metastructures provide advanced control of elastic wave propagation, particularly through their ability to exhibit frequency band gaps where elastic waves cannot propagate. Several metastructure design strategies to realize band gaps in frequency ranges of interest have emerged in recent years. However, the band gap frequencies are fixed at design time by the metastructure geometry and constituent materials. Here, a tunable metamaterial is developed which utilizes the coupled magneto-mechanical response of magnetoactive elastomers (MAE) to enable active control of the band gap frequencies. It is shown that the band gap of a lattice-based metastructure design can be tuned over a continuous frequency range by remote application of a magnetic field. A direct-ink write fabrication method is introduced to fabricate the metastructures from MAEs, which allows this concept to be extended to a vast design space. Our results suggest that the band gap tunability depends not only on the strength of the applied magnetic field, but also on the interaction of the magnetic field and the metastructure geometry. This implies that the combined effects of geometry and magnetic stiffening represent a new design parameter for tunable metastructures, enabling the creation of new smart structures which feature tunable inherent vibration control.

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Phononic crystals (PCs) have been widely reported to exhibit band gaps, which for non-dissipative systems are well defined from the dispersion relation as a frequency range in which no propagating (i.e., non-decaying) wave modes exist. However, the notion of a band gap is less clear in dissipative systems, as all wave modes exhibit attenuation. Various measures have been proposed to quantify the “evanescence” of frequency ranges and/or wave propagation directions, but these measures are not based on measurable physical quantities. Furthermore, in finite systems created by truncating a PC, wave propagation is strongly attenuated but not completely forbidden, and a quantitative measure that predicts wave transmission in a finite PC from the infinite dispersion relation is elusive. In this paper, we propose an “evanescence indicator” for PCs with 1D periodicity that relates the decay component of the Bloch wavevector to the transmitted wave amplitude through a finite PC. When plotted over a frequency range of interest, this indicator reveals frequency regions of strongly attenuated wave propagation, which are dubbed “fuzzy band gaps” due to the smooth (rather than abrupt) transition between evanescent and propagating wave characteristics. The indicator is capable of identifying polarized fuzzy band gaps, including fuzzy band gaps which exists with respect to “hybrid” polarizations which consist of multiple simultaneous polarizations. We validate the indicator using simulations and experiments of wave transmission through highly viscoelastic and finite phononic crystals.

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