IntroductionRecent years have witnessed significant advancements in acoustic functional materials, with the utilization of acoustic metamaterials and their programmable properties to craft functional hybrid structures. This category of structures encompasses various devices, including those showcasing acoustic negative modulus and refraction1,2,3, acoustic holograms4, acoustic cloaks5,6,7, mode transitions8, and acoustic lenses9,10,11. Yet, it’s worth noting that scatter-based metamaterials comm...