On the band gap universality of multiphase laminates and its applications

Abstract

Shmuel and Band [2016] discovered that all infinite band structures of waves at normal incidence in two-phase laminates are encapsulated in a compact universal manifold. We show that manifolds of higher dimensionality encapsulate the band structures of all multiphase laminates. We use these manifolds to determine the density of gaps in the spectrum, and prove it is invariant with respect to certain properties. We further demonstrate that these manifolds are useful for formulating optimization problems on the gaps width, for which we develop a simple bound. Using our theory, we numerically study the dependency of the gaps density and width on the impedance and number of phases. Finally, we show that in certain settings, our analysis applies to non-linear multiphase laminates, whose band diagram is tunable by finite pre-deformations. Through simple examples, we demonstrate how the universality of our representation is useful for characterizing this tunability in multiphase laminates.

On the universality of the frequency spectrum and band-gap optimization of quasicrystalline-generated structured rods

“…The compact representation of the frequency spectrum on T i is now used to formulate rigorously and solve two types of optimization problems in periodic quasicrystalline-generated rods. We focus on the case of F 3 for which analytical representations of the boundaries of the band gaps are available, but the same approach can be easily applied to higher-order cells with the aid of implicit expressions similar to those obtained in [27].…”

“…where n and m are two whole numbers satisfying condition (3.9). The invariance of T 3 and D 3 with respect to the transformations (3.5), together with the conditions A ∈ C − l and B ∈ C + l , provides the following system of implicit equations The illustrated method can be easily applied to cells of higher order through the general approach developed in [27], where analytical expressions for the boundaries of the band gap subregions of periodic laminates with an arbitrary number of phases are derived. This original procedure provides several fundamental advantages with respect to the standard optimization methods based on the numerical evaluation of the frequency spectrum.…”

Flexural wave absorption by lossy gradient elastic metasurface

“…Fortunately, similar methods (Willis, 2016;Srivastava, 2016), which are also called mode-coupling methods for consistency, had been used in elastic waves to study negative refraction of anti-plane shear waves at a plane interface between a homogeneous elastic half-space and a layered periodic composite. Recently, these methods (Lustig et al, 2019;Lustig and Shmuel (2018); Mokhtari et al, 2019;Mokhtari et al, 2020) had been extended to study the scattering of in-plane elastic waves.…”

Symmetry and degeneracy of phonon modes for periodic structures with glide symmetry

“…Many of the aforementioned works are on the wave propagation behavior with a focus on the formation and/or tunability of phononic band gaps Chen et al, 2017aChen et al, , 2017bJavid et al, 2016;Lustig and Shmuel, 2018;Trainiti et al, 2016Trainiti et al, , 2015Parnell, 2017a, 2017b).…”