Tuning of Bandgap Structures in Three-Dimensional Kagome-Sphere Lattice

In this manuscript, acoustic wave propagation in a novel three-dimensional porous phononic crystal-Kagome lattice, is studied by using finite element method. Firstly, a Kagome-sphere structure is established based on Kagome truss. For lattice with fixed rods (sphere radius varied) or fixed spheres (rod radius varied), the band structures are calculated in order to clarify the influence of geometrical parameters (sphere and rod sizes) on the bandgap characteristics in Kagome-sphere lattice. The vibration modes at the band edges of the lowest bandgaps are investigated with the aim to understand the mechanism of the bandgap generation. It is found that the emergence of the bandgap is due to the local resonant vibration of the unit cell at the adjacent bands. The width and position of this bandgap can be tuned by adjusting the geometrical parameters. An equivalent mass-spring model is proposed and the equivalent system resonance frequency can be evaluated which predicts well the upper and lower edges of the complete bandgaps. Moreover, the critical geometrical parameter is formulated which gives the critical geometrical condition for the opening of the complete bandgaps. The results in this paper are relevant to the bandgap structure design of three-dimensional porous phononic crystals (PPCs).