This paper investigates a physics-based hybrid machine learning method that integrates the transfer matrix method (TMM) with a feedforward neural network (FNN) (referred to as TMM-FNN) for analyzing the frequency band structures and band-gaps of Love-Bishop (LB) elastic wave propagation in a graphene origami-enabled phononic crystal (PnC). The PnC consists of periodically repeated unit-cells, each composed of two distinct sections: a pure solid section and a graphene origami-reinforced section. A modified micromechanical model is adopted to estimate the effective properties of the graphene origami-reinforced section. The hyperparameters of the proposed TMM-FNN are optimized to predict the rapid and accurate frequency dispersion curves, as well as both partial and complete band-gaps. Continuity conditions at layer interfaces, together with the Bloch–Floquet periodicity conditions, are enforced to derive the dispersion relations in terms of Bloch wave numbers. The capability and high performance of the proposed TMM-FNN method are demonstrated in predicting both low- and high-frequency band structures. The effects of key parameters on partial and complete frequency band-gaps are investigated in detail using the predicted frequency band structures over a wide frequency range. Compared with existing classical methods, the proposed TMM-FNN achieves high accuracy at a lower computational cost (lower processing time).

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