Towards accurate modeling of the Tachi-Miura origami in vibration isolation platform with geometric nonlinear stiffness and damping

This paper investigates the accurate modeling issue for a class of origami-type dynamic systems with simultaneous kinematical restraint, multi-parameter coupling, and geometric nonlinearity. Based on the geometric relationship, the vertical displacement is transformed into the main variable to characterize the motion of the origami system, and the auxetic property is demonstrated. By using equivalent principle and rigid-foldable origami theory, the negative stiffness is obtained and its formation mechanism is revealed. The accurate dynamic model with consideration of stiffness and damping nonlinearities induced by the periodically nonlinear arrangement is established via Lagrange equation. Then, the origami mechanism is employed in the vibration isolation system to realize quasi-zero-stiffness (QZS) characteristic, and the dynamic behaviors of origami-type isolator subjected to base excitation and force excitation are conducted. A series of simulation studies are provided to validate the superior isolation performance of the designed isolator and the positive effect of the geometric nonlinearity. The proposed accurate modeling framework can be extended to other origami mechanisms and their applications, which can provide powerful theoretical support to the development of origami.