A graded negative refraction-index phononic crystals plate lens for focusing A0 mode Lamb wave and energy harvesting

Abstract In this paper, a method of rotating scatterers was used to design a graded negative refraction index phononic crystal (GNRI PC) plate lens. The present plate lens contains the periodic perforated three-fan holes as the scatterers in the epoxy plate matrix. For a given rotation angle of the scatterer, the rotation would result in a variation of the second A0 band dispersion curve, which is related to a specific negative refraction index. Based on the Snell’s law, the negative refraction index was calculated by utilizing the equifrequency contour and wave vector space for the different rotation angle. Then, the graded negative refraction index plate lens was designed by the specific distribution of the rotation angle of the scatterer. The results show that the plate lens exhibits an obvious focus efficiency in the work frequency range from 16 kHz to 19 kHz. The influence of the work frequency and the dimension of the lens on the focal length was also discussed. Combining with the present plate lens, the energy harvesting analysis was performed numerically, and the energy harvesting efficiency with the plate lens is about 10.5 times larger than that without a lens. This work provides a new way to fabricate GNRI PC plate lens and energy harvesting devices.