Reflection and Refraction of SH Waves at an Interface between a Phononic Crystal and a Homogeneous Solid

摘要

Phononic crystals are periodic composites with frequency ranges in which propagation of elastic waves is forbidden. The existence of these frequency ranges, which are named as frequency band gaps, suggests wide potential applications of the phononic crystals in many fields. Once a phononic crystal is bonded or in contact with other materials or structures, the reflection and refraction at the interface would occur. The purpose of this paper is to explore the propagation characteristics of harmonic SH waves at the interface between a homogeneous solid and a one-dimensional phononic crystal. The effects of wave frequencies on the refraction coefficients are investigated based on the band structures of the phononic crystal obtained by the plane wave expansion method. The results show that for lower frequencies, most part of the energy is reflected into the homogeneous solid and that the frequency has little effects on the energy distribution at the interface. While for higher frequencies, SH waves cannot propagate in some directions because of the existence of the directional band gaps, which results in the discontinuity in the refraction coefficient curve. For waves propagating through the interface, the higher the frequency is, the smaller the refraction coefficient is.