In this paper, a discretized multi-freedom-degree (DMFD) model is presented to predict the lowest locally resonant (LR) band gap in phononic structures. The DMFD model is adopted to improve the accuracy and the application of previous conventional prediction models. Firstly, the model is applied to the one-dimensional ternary LR structure to show the improvement in precision that is independent of the decrease of the density of the scatterer. Then, the model is extended to the evaluation of the resonance frequencies in a two-dimensional binary LR structure, and the estimates from the present model, which are in good agreement with the previous results, verify our model. Each parameter in the DMFD model allows a clear physical insight into the band-gap mechanism. This model could provide a pre-estimation of the lowest gap of binary and ternary LR structures.
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