Ultra-broadband wave attenuation performance in the low band achieved by a simple X-shaped elastic metamaterial

Abstract Locally resonant (LR) elastic metamaterials, characterized by unique bandgap (BG) properties, provide an effective solution for controlling low-frequency noise and vibrations. Inspired by kirigami design principles, this study proposes a simple X-shaped elastic metamaterial plate (XSEMP) containing an LR metastructure. By integrating Bloch’s theorem with the finite element method, the band structure of the X-shaped unit cell is analyzed and the vibration attenuation performance is evaluated along with the BG simulation results using transmission loss spectra. A comprehensive BG analysis method is developed by introducing vibration modes, iso-frequency curves, group velocity, phase velocity, and isolation properties. This approach provides theoretical insights into the underlying mechanisms and relationships that control the opening and closing of BG, wave propagation, and vibration attenuation. Genetic algorithms are combined with BG topology optimization, using an improved adaptive genetic algorithm for on-demand, reverse-engineered adjustment of optimal BG structures. The results demonstrate that the XSEMP has excellent complete ultra-wide BG in the low-frequency subwavelength range and attenuation properties of multi-band elastic waves. This research provides new perspectives for achieving vibration and noise reduction in low-frequency and multiple wide bands, simplifying the design of elastic metamaterials, and optimizing the topology of BG.