Topological design of 3D phononic crystals for ultra-wide omnidirectional bandgaps

As a unique kind of artificial periodic composite materials, phononic crystals have attracted the wide attention in recent years. Unremitting efforts have been made to investigate the potential existence of phononic bandgaps, which can be used to manipulate the propagation of acoustic/elastic waves. This paper proposes a new topology optimization algorithm to achieve the optimised bandgap structures of 3D phononic crystals based on fixed-grid finite element method (FEM) and evolutionary procedure. The maximum normalised gap ratio obtained is as large as 97% between the 12th and 13th order of bands, with the optimised structure of tungsten carbide spheres embraced in epoxy matrix. Symmetric unit cells for simple cubic (SC) lattice are presented for the specified bandgaps to validate the effectiveness of the proposed optimization algorithm for designing 3D phononic bandgap crystals. Meanwhile, the proposed topology optimization represents structures with clear topologies and smooth boundaries.