Analysis of Surface Acoustic Waves in Piezoelectric Phononic Crystals Using Hierarchical Cascading Technique

Two-dimensional (2D) piezoelectric phononic crystals (PnCs) are a kind of artificial composite materials, which have been paid close attention to because of their special transmission characteristics. The calculation of the transmission coefficient of 2D PnCs has always been a problem of large computational complexity with precise methods, and low accuracy with phenomenological methods. To reduce computational time with precise method, hierarchical cascade technique (HCT) combing space-wavenumber analysis was proposed to analyze transmission coefficient of surface acoustic wave in PnCs. By cascading unit blocks, this method avoids amount of matrix calculation. Unit model is built by FEM, and the frequency domain response of entire structure is obtained by cascading these unit blocks with HCT. The displacement distribution is got through the inverse process of cascading. Combining the space-wavenumber Fourier transform, the incident wave and the transmitted wave are then accurately obtained. Thus transmission coefficient is obtained.