Band structures of elastic waves in two-dimensional eight-fold solid-solid quasi-periodic phononic crystals

Combined with the supercell method, band structures of the anti-plane and in-plane modes of two-dimensional （2D） eight-fold solid-solid quasi-periodic phononic crystals （QPNCs） are calculated by using the finite element method. The influences of the supercell on the band structure and the wave localization phenomenon are discussed based on the modal distributions. The reason for the appearance of unphysical bands is analyzed. The influence of the incidence angle on the transmission spectrum is also discussed.