Parametric analysis: Compressibility of rubber on bandgap for phononic crystals

The capacity of Phononic crystals (PCs) to form bandgaps (BGs) that limit the transmission of elastic/acoustic waves is a key property that is particularly beneficial for vibration/sound isolation and signal processing. In this work, a parametric analysis of Poisson’s ratio of rubber, and the density, geometry and size of scatterer on the BGs of porous, solid/solid, fluid/solid and solid/fluid PCs is presented. Based on the simulation results, it is found that the width of the first absolute bandgaps (FABGs) of porous PCs is not necessarily proportional to the porosity due to the pore shape; when Poisson’s ratio of compressible and incompressible rubber is increased, the FABG width of porous PC decreases dramatically. In addition, the FABGs of solid/solid PCs are strongly dependent on whether the rubber is a matrix or scatterer; the fluctuation of the FABGs is also highly related to the density of the solid. Fluid–structure PCs have smaller FABGs than porous and solid/solid PCs, and these FABGs usually occur within higher-order energy bands. Rubber compressibility significantly affects the FABGs of porous and solid/solid PCs, but almost not fluid-structural PCs. The results presented in this work offer guidance to tune the BG and design acoustic devices in various practical applications such as noise and vibration insulators.