A symmetric substructuring method for analyzing the natural frequencies of conical origami structures

Conical origami structures are characterized by their considerable out-of-plane stiffness and energy-absorption capacity. Previous investigations have commonly focused on the static characteristics of these lightweight structures. However, efficient analysis of the natural vibrations of these structures is pivotal for designing conical origami structures with programmable stiffness and mass. In this paper, we propose a novel method to analyze the natural vibrations of such structures by combining a symmetric substructuring method (SSM) and a generalized eigenvalue analysis. SSM exploits the inherent symmetry of the structure to decompose it into a finite set of repetitive substructures. In doing so, we reduce the dimensions of matrices and improve the computational efficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis. The simulated results of pin-jointed models implemented using finite element analyses are used to validate the computational results of the proposed approach. Moreover, the parametric analysis of the structures demonstrates the influences of the number of segments along the circumference and the radii of the cone on the structural mass and natural frequencies of the structures. Furthermore, a comparison between six-fold and four-fold conical origami structures and the influence of various geometric parameters on their natural frequencies is presented. This work provides a strategy for efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contribute to the efficient design and customization of origami structures with programmable stiffness.