Coupled-translation-rotation mechanics model and design for broadband wave energy conversion in anisotropic multiphase metamaterials

Elastic metamaterials typically display anisotropic scattering behavior which mainly stems from high-order modes linked to shear and rotation deformations, thus complicating the characterization of the scattering behavior. However, most existing mass-spring models can only describe the coupled in-plane motions of longitudinal and transverse waves, which naturally ignores the essential rotations. Considering the pure translation and coupled-translation-rotation motions, this study proposes two spring-interconnected mass-in-mass models with rotational symmetry, featuring 2-degree-of-freedom (2-DOF) and 3-DOF anisotropic configurations respectively. For an incident longitudinal wave, the scattered transverse wave energy in these models is theoretically demonstrated at a specific rotation angle of spring. The established scattered elastic wave energy theory associating the dynamic response with structural parameters indicates that the higher scattering energy conversion of metamaterials can be achieved if two polarization components of translation and rotation are considered simultaneously. Comparing the scattering energy conversion capabilities of uni-layer and bi-layer models reveals that the bi-layer 3-DOF anisotropic model promotes the higher-efficiency low-frequency scattering energy conversion by reducing the dynamic effective stiffness. Variations in the scattering conversion coefficient with mass and aspect ratio clarify that lightweight components and soft springs are beneficial for efficient scattering energy conversion over a low-frequency broadband range. Furthermore, by investigating damping on energy distribution of 3-DOF anisotropic model, the underlying mechanism for capturing longitudinal wave energy is identified as integrating low-frequency scattering for energy conversion with high-frequency mechanisms for energy dissipation. Consequently, the 3-DOF anisotropic model achieves reflection-free wave energy across a broadband frequency range with a small amount of loss. To validate the proposed theory, model, and the underlying mechanism, anisotropic multiphase metamaterials are inversely designed to simultaneously deliver broadband wave-energy dissipation and high load-bearing capacity. Scattering characteristic analysis indicates that the metamaterials exhibit strong anisotropy and broadband energy conversion capability, with further validation by simulations and experiments. The present study establishes a foundation for high-load-bearing metamaterial-based elastic-wave absorbers and isolators.