Although auxetic metamaterials are generally light in weight, strong in compression and superior in energy absorption, less research has focused on their low-frequency bandgap realization and inverse structural design. Moreover, broadening the width of bandgap of auxetic metamaterials keep challenging as well in practical low-frequency applications. To broaden their applications, this work provides a new auxeticity-based composite resonator design by filling hard engineering material into the soft auxetic structure perforated by orthogonally-arrayed peanut-shaped holes to achieve ultra-wide low-frequency bandgap. The soft material is silicone rubber and the hard material may be concrete, steel or plumbum. Firstly, the wave propagation mechanics of the present composite structure is studied and then the bandgap characteristics are thoroughly investigated by parameter analysis. On this basis, a machine learning (ML) method combining the standard back-propagation neural network and genetic algorithm is proposed for bandgap prediction and inverse structural design. Results indicate that the present composite structure performs well in generating ultra-wide low-frequency bandgap, i.e. [11.35, 24.07] Hz, and the relative bandgap width reaches 71.76 %. Moreover, the present ML method is effective in the forward prediction of bandgap and the inverse structure design fitting the specific bandgap requirement. For the created optimal designs, the ML method and the finite element simulation can give similar results, and the maximum relative error between them is just about 5 %, which verifies the accuracy of the ML design method. This work provides a new way to realize the structural design of auxeticity-based acoustic metamaterials with low-frequency and broad bandgap.
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