3-D phononic crystals with ultra-wide band gaps

Abstract

In this paper gradient based topology optimization (TO) is used to discover 3-D phononic structures that exhibit ultra-wide normalized all-angle all-mode band gaps. The challenging computational task of repeated 3-D phononic band-structure evaluations is accomplished by a combination of a fast mixed variational eigenvalue solver and distributed Graphic Processing Unit (GPU) parallel computations. The TO algorithm utilizes the material distribution-based approach and a gradient-based optimizer. The design sensitivity for the mixed variational eigenvalue problem is derived using the adjoint method and is implemented through highly efficient vectorization techniques. We present optimized results for two-material simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC) crystal structures and show that in each of these cases different initial designs converge to single inclusion network topologies within their corresponding primitive cells. The optimized results show that large phononic stop bands for bulk wave propagation can be achieved at lower than close packed spherical configurations leading to lighter unit cells. For tungsten carbide - epoxy crystals we identify all angle all mode normalized stop bands exceeding 100%, which is larger than what is possible with only spherical inclusions.

Fast Domain Wall Motion Governed by Topology and Œrsted Fields in Cylindrical Magnetic Nanowires

“…However, there are limits regarding what can be achieved with materials, or realized with device fabrication. An alternative strategy entails considering a specific topology in order to develop the desired properties of a system, yielding diverse applications such as the design of wide-band-gap photonic crystals [2] and the control of flow of macromolecules [3], or novel theoretical methods such as for the description of defects [4], or intringuing 3D vector-field textures such as hopfions and torons [5]. As regards magnetism, unusual properties resulting from topological features have been predicted, such as the existence of a domain wall (DW) in the ground state of a Moebius ring [6], or the non-reciprocity of spin waves induced by curvature and boundary conditions in nanotubes [7].…”

Accordion-like metamaterials with tunable ultra-wide low-frequency band gaps

“…The reported data refer to three-dimensional or two-dimensional (in-plane waves) configurations of continuous (bold lines) or cellular (dashed lines) structures. The band-gap widths have been re-calculated for a unit cell size of 10mm, based on the data provided in the original works [17][18][19][20][21]35], for a uniform comparison.…”

“…The unit cell size is h uc =10 mm and the material volume fraction V m are indicated for each structure. The initial data are taken from [17] for coated Au circles in epoxy; [21] for convex and concave holes in copper; [35] for cross-like holes in a polymer; [20] for polymeric spheres joined by ligaments; [19] for Tg scatterers in epoxy; [18] for Si strip with Tg pillars. + + versus frequency f for an accordion-like meta-chain (30 unit cells).…”

“…The local resonance effect is induced by coated inclusions or pillars, increasing the total structural weight. In this case, wave attenuation is efficient only at the resonator eigenfrequencies and abruptly decreases away from them [5,14,[17][18][19]. Therefore, broadband control of low-frequency waves using lightweight structures remains a challenge.…”

A polynomial‐based method for topology optimization of phononic crystals with unknown‐but‐bounded parameters

“…Meanwhile, Li et al used the bidirectional evolutionary structural optimization in conjunction with the homogenization method for the topology optimization of cellular PnCs with a bulk or shear modulus constraint. Recently, Lu et al used the gradient‐based topology optimization (GTO) method to obtain 3D PnCs with ultrawide normalized all‐angle and all‐mode BGs. Among these aforementioned methods, some of them that require the gradient information and the sensitivity calculation are called the GTO methods.…”