Negative elastic wave refraction and focusing regulation of single-phase solid phononic crystals

Abstract

This paper presents the design of a single-phase solid phononic crystal (PnC) structure featuring a regular hexagonal perforation pattern. The structure manifests three negative refraction bands, encompassing one for transverse waves and two for longitudinal waves, thereby enabling simultaneous control of shear and longitudinal waves. Due to the high symmetry of the triangular lattice, the equal frequency curves corresponding to the negative refraction band approach circular shapes, suggesting a nearly isotropic negative refraction effect. This negative refraction effect is achieved through specific mass resonance modes closely related to the porous structure designed in this paper. Initially, we analyze the band structure of the PnC, followed by designing the PnC plate structure to achieve negative refraction control for transverse waves at a frequency of 32.4 kHz, with a negative refraction index of −1. Additionally, negative refraction control for longitudinal waves is attained at frequencies of 44 and 64.54 kHz. Subsequently, we scrutinize the influence of various conditions on negative refraction, including different structural parameters, incident angles, and operating frequencies, while verifying the robustness of the designed phonon crystal structure. Leveraging the negative refraction characteristics of the structure, we construct an elastic wave lens to achieve perfect imaging of shear and longitudinal waves. Finally, employing finite element simulation and analyzing focusing imaging characteristics with different source positions, we validate that the results closely align with theoretical expectations. The solid PnC structure designed in this study holds significant potential for applications in the fields of elastic wave imaging.