Trampoline metamaterial: Local resonance enhancement by springboards

Abstract

We investigate the dispersion characteristics of locally resonant elastic metamaterials formed by the erection of pillars on the solid regions in a plate patterned by a periodic array of holes. We show that these solid regions effectively act as springboards leading to an enhanced resonance behavior by the pillars when compared to the nominal case of pillars with no holes. This local resonance amplification phenomenon, which we define as the trampoline effect, is shown to cause subwavelength band gaps to increase in size by up to a factor of 4. This outcome facilitates the utilization of subwavelength metamaterial properties over exceedingly broad frequency ranges.Phononic crystals and locally resonant acoustic/elastic metamaterials have been the focus of extensive research efforts in recent years due to their attractive dynamical characteristics, such as the possibility of exhibiting band gaps. In a phononic crystal, band gaps are generated by Bragg scattering for which an underlying constraint is that the wavelength has to be on the order of the lattice spacing. 1,2 In a locally resonant acoustic/elastic metamaterial, on the other hand, band gaps may be generated by the mechanism of hybridization between local resonances and the dispersion properties of the underlying medium, and this in turn may take place at the subwavelength regime. 3 While in principal periodicity is not a necessity in a metamaterial, the introduction of the locally resonant elements in a symmetric fashion enables intrinsic, unitcell based, description of the wave propagation characteristics, in addition to attaining the benefits of order and compactness. The presence of periodicity, in itself, produces direction-dependent frequency bands and band gaps (caused by Bragg scattering). These unique dispersion properties may sufficiently be utilized in numerous applications involving wave filtering, 4-6 localization, 7,8 guiding, 8,9 focusing, 10-12 collimation, 13,14 among others. The added feature of local resonance, however, gives rise to a qualitatively different type of dynamical behavior, such as negative effective elastic moduli and/or density, 15-18 along with the possibility of generation of subwavelength band gaps. 3 The applications of locally resonant acoustic/elastic metamaterials are, in turn, far from conventional, e.g., subfrequency wave isolation, 19 subwavelength focusing and imaging, 20,21 and cloaking, 22 to name a few. Crossing the boundaries of acoustics and elasticity, our group at CU-Boulder has recently proposed the utilization of locally resonant metamaterials for the control of heat in a semiconducting thin-film. 23 Regardless of the application, one of the generally desirable characteristics is for the metamaterial to exhibit a large band gap. While the problem of unit-cell optimization for maximum band-gap size has been actively pursued a) mih@colorado.edu for phononic crystals, 6,24,25 less work has been done in exploring new approaches for band-gap enlargement in locally resonant acoustic/elastic metamaterials.One...

Phonon and heat transport control using pillar-based phononic crystals

“…To further broaden the frequency range, researchers proposed the hybrid hole/pillar-based PnCs [44,45]. Such hybrid PnCs take advantages of both wide Bragg gaps of hole-based PnCs and multiple high-frequency bandgaps of pillar-based PnCs.…”

Flow stabilization by subsurface phonons

“…The inertial, elastic and damping properties of the selected materials are provided in appendix A. The choice of unit-cell length is not constrained in the current investigation; future work will aim to shorten it by exploiting established band-gap-lowering mechanisms, such as using local resonators [22,29]. By employing Bloch's theorem [30] (see problem 1 in appendix A), we obtain dispersion curves for this unit-cell configuration, which appropriately comprise a stop band covering the range 1652 ≤ ω ≤ 2102 Hz, as shown in figure 1b.…”

“…One realization is shown at the bottom of figure 1a, in which a segment of the bottom surface of a flow channel with otherwise all-rigid walls is replaced with a one-dimensional elastic phononic crystal consisting of alternating layers stacked perpendicularly underneath. This one-dimensional two-layer per unit-cell configuration is chosen for its simplicity; however, two-dimensional or three-dimensional unit cells with complex topologies such as those considered in [21,22] property that we use in a phononic material is that it possesses a frequency band structure, consisting of stop bands (band gaps) and pass bands, and that the phase of an incident wave travelling in the medium is altered based on whether it falls within a stop band or a pass band [23]. Specifically, a stop band admits out-of-phase waves and a pass band retains the phase.…”

Focusing of the lowest-order antisymmetric Lamb mode behind a gradient-index acoustic metalens with local resonators

“…Besides, depending on the shape and dimensions of the resonant inclusions, the resonances may arise at a very low frequency as compared to the Bragg gap, in a region of the reduced Brillouin zone where effective theories apply. This has been demonstrated both theoretically and experimentally, with 2D PCs made of an array of cylindrical pillars regularly erected on a homogeneous thin slab [44][45][46][47][48][49][50][51][52]. This last structure deserves special attention.…”

“…Metamaterials with local resonances generally fulfill this latter requirement since they may display very slow sound velocity, at least near resonances [9,[18][19][20][21][42][43][44][45][46][47][48][49][50][51][52]. Besides, depending on the shape and dimensions of the resonant inclusions, the resonances may arise at a very low frequency as compared to the Bragg gap, in a region of the reduced Brillouin zone where effective theories apply.…”