On the nonlinear dynamics of a Kresling-pattern origami under harmonic force excitation

Kresling origami-inspired cylindrical structures have received considerable attention due to their effective deployment characteristics, programmable dual-directional and multifunctional properties, along with their ability to support loads. The Kresling origami investigations to date have focused mostly on their geometry, kinematics, and quasi-static mechanics. While recent works have started to uncover the Kresling origami's transient deployment dynamics and linear vibration/wave propagation features, the rich nonlinear dynamics of Kresling origami-inspired structures under consistent external excitations have yet to be examined and understood. Given that Kresling origami elements are highly nonlinear so their dynamic responses can be extremely complex under external disturbances, and the fact that in many applications they are embedded in mechanical systems that are continuously excited, such as in robotics, air and ground vehicles, and impact, noise, and vibration isolation structures, this is an important and nontrivial research issue that needs to be addressed. To advance the state of the art, the goal of this research is to explore and uncover the nonlinear dynamics of Kresling origami-inspired tubular structures under consistent forced excitations, in particular harmonic loadings. Time and frequency domain analyses are performed and bifurcation diagrams are developed and analyzed for a range of forcing amplitudes and frequencies. This research reveals the complex responses of Kresling origami-inspired systems, i.e., existence of multiple period-1 attractors, period -n (n > 1) attractors, jump from one attractor (limit-cycle) to another attractor, and presence of chaotic attractors for a range of input forcing parameters. The noteworthy result of this study also concerns a synchronization of the origami cylinder's steady-state axial and rotational (twist) displacements. Without such a forced nonlinear dynamic analysis, these findings have not been and cannot be discovered in previous studies. The insights and knowledge uncovered in this investigation are valuable in raising awareness and providing guidance in the design and control of Kresling origami based structures for realistic engineering operations, where external dynamic disturbances are often unavoidable. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

Kresling origami-inspired cylindrical structures have attracted attention due to their effective deployment characteristics, programmable properties, and load-bearing ability. However, the nonlinear dynamics of these structures under consistent external excitations have not been thoroughly studied. This research explores the nonlinear dynamics of Kresling origami-inspired tubular structures under forced excitations and reveals complex responses, including period-1 attractors, period-n attractors, transitions between attractors, and chaotic attractors. The findings provide valuable insights for the design and control of these structures in practical engineering operations.