Modelling and analysis of large periodic origami structures for local vibrations

Abstract

In this paper, a novel framework is proposed for the structural analysis of large origami structures. The first order shear deformation theory of plates (FSDT) is employed to consider the stiffness of the origami facets and the folds stiffness is modeled via six linear and rotational springs at the intersections of the facets. The framework enables to predict the response of the entire elastic origami tessellation, by solving for the response of a unit cell under periodic boundary conditions. As a case study, a composition of four facets that its repetition forms the entire domain of Miura-ori tessellations is chosen as the unit cell. Then, the response is generated through solving a system of 20 linear-coupled PDEs subject to 80 boundary conditions. The results are generated numerically using generalized differential quadrature (GDQ) and finite element (FE) analysis. Via use of the framework, for the first time the effects of microstructure properties on the local vibration response of different Miura-ori tessellations are studied. Specifically, the effects of the base material, the facets geometry and the folds stiffness on the local vibration response of the structure are studied. Particularly, we show the existence of mode crossings (different mode shapes being excited with the same frequency) in the local vibration response of different Miura-ori unit cells that is highly affected by the microstructural characteristics. The results generated here can be used for designing and tailoring origami structures for high-end applications.