Mechanical Response and Low-Order Wave Propagation of Curved-Rod Compression–Torsion Coupled Metamaterials

Compression–torsion coupled metamaterials provide a geometry-driven approach for motion conversion and wave regulation. This study proposes a spatial curved-rod compression–torsion coupled metastructure and develops a reduced-order equivalent stiffness model with axial displacement and rotational angle as the generalized degrees of freedom. The equivalent stiffness matrix, derived from the curved-rod centerline geometry through a strain-energy formulation, is incorporated into a one-dimensional Bloch model to characterize low-frequency wave propagation. The results show that the off-diagonal coupling stiffness governs the compression-induced rotational response of the unit cell and significantly affects the frequencies and modal compositions of the two lowest dispersion branches. Finite element simulations and experiments validate the predicted stiffness and compression–torsion response, while acceleration transmissibility measurements of a finite periodic chain are consistent with the theoretical dispersion characteristics. The reduced-order model captures the overall behavior of the two lowest branches and clarifies the role of compression–torsion coupling stiffness in branch separation and modal composition, although the higher branch is less accurately predicted owing to the lumped inertia approximation. The proposed design provides a lightweight strategy for low-frequency wave regulation through structural coupling.