Negative refraction of flexural wave propagation on phononic thin plates based on the backward wave effect

Abstract

The negatively refracted flexural wave is explored for phononic thin plates consisting of periodic holes and inclusions based on the effect of backward waves. Dispersion curves of these two types of phononic thin plates are calculated by using the multipole method, and the backward wave effect has been clearly found in their band diagrams. By using multiple scattering simulations, the birefraction phenomenon has been observed in a prism-shaped hole array, whereas single negative refraction has been realized in a prism-shaped inclusion array. The explanations using Snell’s law are presented for the occurrence of birefraction and sole negative refraction. Experiment verifications of birefraction phenomenon show good agreements with both numerical and analytical results. Numerical results also indicate the multiple scattering simulation is an alternative method for observing negative refraction of flexural waves.