Wave propagation in nonlinear locally coupled resonant Kresling origami metamaterials

Origami structures have garnered widespread attention in dynamic research due to their excellent deformability and rich tunable static properties. Among these, the Kresling origami structure is notable for its kinematic coupling characteristics. The unique nonlinear kinematic coupling characteristics of the Kresling origami structure are discussed based on the truss model. A one-dimensional nonlinear locally coupled resonant Kresling origami metamaterial is constructed using spatially antisymmetric arrangements. The outer frame is unaffected by rotation, and the internal oscillator is influenced by both axial displacement and rotation. The equivalent coupling stiffness of the unit cell is theoretically analyzed. By employing the perturbation method, an explicit expression for the dispersion relation of the nonlinear locally coupled resonant system is derived. Furthermore, the impact of the excitation amplitude on the dispersion shifts in the metamaterial is investigated. The solitary wave, which is generated by the first bandgap interval where nonlinearity increases propagation, is captured via time and space Fourier transform analysis. Numerical analysis of the transmission characteristics provides evidence for the accuracy of the theoretically predicted dispersion shifts. Finally, a prototype was fabricated experimentally, qualitatively confirming that the dispersion shifts results from the nonlinear coupling stiffness effect. Overall, the proposed nonlinear Kresling origami metamaterial is promising for advancing dynamic and vibration control applications. Additionally, it offers new insights into the dynamics of nonlinear periodic structures.