Engineering elastic bandgaps in TPMS-based metamaterials via geometric flattening and multi-morphology hybridization

Triply periodic minimal surface (TPMS) architectures have become a prominent class of mechanical metamaterials, largely due to their excellent lightweight load-bearing capability and energy-absorption performance enabled by smooth, continuous, and highly connected geometries. In contrast, their dynamic characteristics remain far less systematically understood. In this work, we present a comprehensive study of 3D elastic-wave dispersion relations and bandgaps for fourteen TPMS-based metamaterials constructed from seven minimal surfaces using two thickening strategies (solid- and sheet-based). Building on these baselines, we further introduce two practical bandgap- engineering routes, geometric flattening and smooth multi-morphology hybridization, and quantify their effects on flexural bandgaps. Our results show that among the fourteen structures, only solid-primitive and solid-neovius support complete bandgaps, whereas sheet-diamond design exhibits no bandgap; the remaining structures predominantly feature directional bandgaps. Geometric flattening leads to a consistent downshift of flexural bandgap frequencies and a reduction in bandgap bandwidth, while multi-morphology hybridization further enables bandgap frequency downshift without requiring a lower volume fraction. The predicted bandgaps are validated through harmonic-response simulations and transmission experiments. Overall, our work offers a quantitative basis for selecting TPMS structures and corresponding volume fractions for vibration suppression panels, and provides engineering methods for future TPMS-based elastic/acoustic metamaterial design.