Design, Analysis, and Optimization of Negative Stiffness in a Kresling-Origami Rod-Hinged Truss

Abstract

Negative stiffness is a unique mechanical phenomenon that arises during the elastic snap-through process after structural instability. It promotes motion, making it particularly advantageous in various specific applications such as damping amplifiers and quasi-zero stiffness isolators. However, to harness its benefits, it is crucial to design and control negative-stiffness structures with precision; otherwise, their introduction may pose risks of system instability, negating the intended advantages. Current negative-stiffness structures present challenges, including a narrow negative-stiffness region and strong nonlinearity, which complicate control. Therefore, this paper aims to explore a research method for a Kresling-origami-inspired negative-stiffness structure to enhance its negative-stiffness characteristics. First, the negative-stiffness characteristics of the Kresling-origami panel, the Kresling-origami rod-hinged truss, and the Kresling-origami beam-buckling structure are compared, highlighting the superiority of the rod-hinged truss in negative-stiffness design. Then, the displacement-rotation coupling motion equations for the rod-hinged truss are derived, the interference conditions during the truss’s motion process are established, and the impact of parameters on the negative-stiffness characteristic is investigated. Finally, the parameter optimization strategy is determined. The results demonstrate that the research method can precisely design the negative-stiffness value at the unstable static equilibrium point, improve the proportion of the negative-stiffness region over the entire stroke, and enhance the linearity and central symmetry of negative stiffness near the unstable static equilibrium point. The findings of this study indicate that the Kresling-origami rod-hinged truss exhibits nonlinear mechanical properties, characterized by prominent negative-stiffness and bistable behavior. This highlights the structure’s superiority in negative-stiffness design. Additionally, the stiffness of the rods can be conveniently adjusted by incorporating different springs within the sliding bars, and the absence of folds or creases removes many limitations on the choice of base materials, making the structure easier to engineer. By employing the proposed optimization method, the negative-stiffness value at the unstable static equilibrium point can be precisely designed. Furthermore, this method enhances the proportion of the negative-stiffness region across the entire stroke and improves the linearity and central symmetry of the negative stiffness near the unstable static equilibrium point. This refinements design facilitates the effective application of negative-stiffness structures in engineering systems such as damping amplifiers and quasi-zero stiffness isolators.