Thickness-Deformation Collaborative Bandgap Control of Deep-Subwavelength Metallic Kirigami Metasurfaces

Three-dimensional Kirigami structures, as large-deformation deep-subwavelength phononic crystals (artificial periodic materials with structural feature sizes much smaller than the acoustic wavelength, enabling miniaturization of acoustic devices), exhibit significant application potential in metal-based acoustic regulation devices. However, the intrinsic coupling mechanism of bandgap regulation under the collaborative effect of thickness and deformation (including the interaction between stiffness anisotropy, modal hybridization, and Bragg scattering) remains insufficiently systematically elucidated. Particularly, the influence of the high stiffness characteristic of metal materials on regulation laws still requires in-depth verification. In this study, commercial pure aluminum (1060 grade) was selected as the research object, and the collaborative regulation mechanism of thickness and tensile deformation on the band structure was systematically revealed through a combination of finite element simulation and experimental validation. Theoretically, an evolution model of modal polarizability (η, a parameter quantifying the dominant degree of out-of-plane vibration modes in structural vibration) was established based on the bending/tensile stiffness ratio (D/A, the key ratio determining the vibration behavior of thin-plate structures), and a critical thickness was clearly proposed as the boundary between effective and ineffective bandgaps. Experimental characterization was conducted to validate the theoretical predictions of bandgap parameters (bandwidth, central frequency) and stress distribution. The results show that there exists an optimal thickness range for efficient bandgap regulation, enabling reversible closure of bandgaps with small tensile deformation. For thin structures, the out-of-plane mode dominates, featuring high bandgap stability but low regulation sensitivity. For thick structures, deep modal hybridization occurs, and the lower limit frequency of the bandgap shifts out of the target frequency range. This study establishes a quantitative correlation framework of "thickness-stiffness-modal-bandgap" for metal-based Kirigami structures, providing a directly applicable theoretical basis for the engineering design of high-performance acoustic regulation devices.