Phononic band gap crystals with periodic fractal inclusions: Theoretical study using numerical analysis

Abstract

A numerical study is conducted using finite difference time-domain analysis to determine the impact of periodic fractal-shaped inclusions on the frequency response of two-dimensional phononic or acoustic band gap crystals. Both solid host with solid inclusions and solid host with fluid inclusions were studied with increasing fractal order iteration or increasing fractal dimensionality for different types of fractals generated from square inclusions in a square lattice formation. Solid-fluid systems showed marked changes in frequency response including increasing multiplicity of bands compared to regular square inclusion shapes. Fractal inclusions in the solid host/fluid inclusion systems studied exhibited the ability to provide band gaps for much longer wavelengths than those of the solid host/solid inclusion systems studied. This behavior was attributed to the possibility of resonant localization effects that a fractal fluid inclusion can exhibit compared to fractal solid inclusions.