TOPOLOGICALLY PROTECTED WAVE TRAPPING IN ACOUSTIC METAMATERIALS

This study explores the phenomenon of acoustic wave trapping in metamaterials by strategically configuring the geometrical properties of unit cells. Unlike topological insulators, where wave propagation is confined to edge states, acoustic wave trapping in structured metamaterials enables energy localization within the bulk region without interacting the edges. To analyze wave propagation behavior, this study employs Floquet periodic boundary conditions to calculate the band structure and mode shapes of longitudinal and transverse waves in infinitely repeated periodic unit cells. By leveraging COMSOL Multiphysics, a comprehensive numerical model is developed, optimizing the geometric and material properties of unit cells by varying the volume fraction to precisely tune Dirac-like cones at the gamma point of the Brillouin zone. This approach allows for precise modulation of band structures, providing control over wave trapping locations by manipulating the occurrence of the Dirac-like cones. A frequency-domain analysis is conducted to examine the wave trapping mechanisms and assess their dependence on structural parameters, such as lattice anisotropy and periodicity while keeping constant material properties. The results demonstrate that the Dirac-like cone significantly influences energy confinement without inducing any displacement at the edge unit cells, allowing the formation of localized high-energy acoustic modes. Additionally, the study investigates the role of bulk structure aspect ratios in enhancing wave localization efficiency. This research proposes a framework for engineering metamaterials with tailored acoustic energy confinement by demonstrating that wave trapping can be achieved through precise tuning of Dirac-like cones, independent of conventional boundary reflections. The results open pathways for next-generation acoustic metamaterials capable of adaptive wave trapping, offering promising applications in medical imaging, structural health monitoring, and advanced acoustic sensing.