Supplementary material from "Improving mass lumping and stiffness parameters of bar and hinge model for accurate modal dynamics of origami structures"

The bar and hinge framework uses truss elements and rotational springs to efficiently model the structural behavior of origami. The framework is especially useful to investigate origami metamaterials as they have repeating geometry which makes conventional finite element simulations very expensive due to a large number of degrees of freedom. This work proposes improvements to the parameters of bar and hinge model within the context of structural dynamics, specifically modal analysis under small deformations, which has not been carried out previously in the literature. A range of low-frequency modes involving origami folding and panel bending deformations that can be accurately captured by the bar and hinge framework are identified. Within this range, bar and hinge parameters like the lumped masses and the rotational spring stiffness values are derived using conservation laws and finite element tests. The best among the proposed schemes is found to predict natural frequencies of the considered origami structures to within ten percent maximum error, improving the accuracy by more than three times from existing schemes. In most cases, the errors in natural frequencies are less than five percent.