Perfect-bandgap tapered nanophononic metamaterial beam for thermal insulation

Solid geometries guide multiple acoustic waves whose polarizations are different owing to the presence of compressional and shear stresses. In the case of a rod, elastic wave polarizations can take four different forms, i.e. compressional, two-directional bending, and torsional modes, which are easily distinguished at low enough frequencies. Supressing such elastic modes is an industrially important issue. Acoustic metamaterials are prime examples of manmade solid media designed to this end. In spite of recent remarkable progress of this field, there is still a need for metamaterial rods or beams for damping, i.e. meta-rods or meta-beams. Moreover, by nanoscale miniaturization of such structures and tailoring for wideband response they could be efficient thermal insulators. In particular, single-material structures are desirable for easy manufacturing. Perfect bandgap meta-rods have often been achieved by combining several materials, [1] - [3] although some single-material phononic-crystal rods or beams with perfect bandgaps have been reported [4] , [5] . Recently, we designed a single-material perfect acoustic bandgap meta-beam and meta-rod for the kHz range, and experimentally demonstrated them [6] , [7] . In the present study, by means of numerical simulations and experiments on a macroscopic scale we present the use of tapered meta-beam structures consisting of five unit cells of slowly varying size that extend the phonon propagation frequency gap significantly, opening up the potential for nanophononic applications in thermal insulation.