Search

Recent advances in origami science and engineering have particularly focused on the challenges of dynamics. While research has primarily focused on statics and kinematics, the need for effective and processable dynamic models has become apparent. This paper evaluates various dynamic modelling techniques for rigid-foldable origami, particularly focusing on their ability to capture nonlinear dynamic behaviours. Two primary methods, the lumped mass–spring–damper approach and the energy-based method, are examined using a bistable stacked Miura-origami (SMO) structure as a case study. Through systematic dynamic experiments, we analyse the effectiveness of these models in predicting bistable dynamic responses, including intra- and interwell oscillations, in different loading conditions. Our findings reveal that the energy-based approach, which considers the structure's inertia and utilizes dynamic experimental data for parameter identification, outperforms other models in terms of validity and accuracy. This model effectively predicts the dynamic response types, the rich and complex nonlinear characteristics and the critical frequency where interwell oscillations occur. Despite its relatively increased complexity in model derivation, it maintains computational efficiency and shows promise for broader applications in origami dynamics. By comparing model predictions with experimental results, this study enhances our understanding of origami dynamics and contributes valuable insights for future research and applications. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

The main challenges in identifying time-varying systems are to extract the inherent model structure and formulate a generic approach for various time-varying processes. In this article, a local linear neuro-fuzzy networks based approach is proposed for the first time to tackle this issue. The basic idea is to utilize the superior approximation capability of the fuzzy neural networks to expand the unknown time-varying parameters so that various nonlinear and discontinuous processes can be captured. In addition, the local linear model tree optimization algorithm is incorporated in our approach to optimize the network architecture. On one hand, the least number of neurons corresponding to the time-varying parameters can be automatically determined, thus avoiding the superfluous bases and the troublesome overfitting problem; on the other hand, the optimized distribution of the neurons could significantly increase the interpretability of the results, thus contributing to locating the domains where the parameters exhibit strong nonlinearity or change sharply. Moreover, we demonstrate that our approach could simultaneously extract the parsimonious model structure while identifying the time-varying parameters, without adding additional procedures or increasing computation burden. Considering the generality and the unique merits, our proposed approach could significantly advance the applications of artificial neural network techniques in system identification. [ABSTRACT FROM AUTHOR]

Self-locking origami structures are characterized by their piecewise linear constitutive relations between force and deformation, which, in practice, are always completely opaque and unmeasurable: the number of piecewise segments, the positions of non-smooth points, and the linear parameters of each segment are unknown a priori. However, acquiring this information is of fundamental importance for understanding the origami structure's dynamic folding process and predicting its dynamic behaviors. This, therefore, arouses our interest in adopting a dynamical identification process to determine the model and to estimate the parameters. In this research, based on the piecewise linear assumption, a physically-interpretable neural-fuzzy network is built to correlate the measured input and output data. Unlike the conventional approaches, the constructed neural network possesses specific physical meaning of its components: the number of neurons relates to the number of piecewise segments, the coefficients of the local linear models relate to the parameters of the constitutive relations, and the validity functions relate to the positions of non-smooth points. By addressing several examples with different backgrounds, the network's underlying data training methods are illustrated, including the local linear optimization for linear parameters, nested optimization for nonlinear partitions, and Local Linear Model Tree optimization for model selection. Noting that the tackled origami problem holds strong universality in terms of the unknown piecewise characteristics, the proposed approach would thus provide an effective, generic, and physically significant means for handling piecewise linear dynamical systems and meanwhile bring fresh vitality to the artificial neural network research. [ABSTRACT FROM AUTHOR]