Triply periodic minimal surfaces (TPMS) lattice structures present outstanding properties such as lightweight, high strength, energy absorption, and wave propagation control, which are extensively investigated in recent years. However, one of the main challenges when designing TPMS is the proper selection of cell type and volume ratio in order to obtain the desired properties for specific applications. To this aim, this work provides a comprehensive numerical study of bandgap’s formation in the sub-2 kHz frequency range for the seven major cell type TPMS structures, including Primitive, Gyroid, Neovius, IWP, Diamond, Fischer–Koch S, and FRD, for a comprehensive range of volume ratios. Results show that these seven TPMS structures present a complete bandgap between the 3rd and 4th dispersion curves. The width of the bandgap is strongly dependent of the TPMS lattice and the widest bandgaps are seen on the Neovius and Primitive-based lattice (reaching a maximum width of 0.458 kHz and 0.483 kHz, respectively) for volume ratios over 0.3. Below this volume ratio, the bandgap of the Primitive structure becomes negligible, and the Neovius and IWP structures are the best candidates among the 7 tested TPMS cases. The central frequency of the bandgaps is less sensitive to the lattice and are predominantly tailored by the volume ratio. With this study, we demonstrate that the proper selection of the periodic cell type and volume ratio can tailor the bandwidth of complete bandgaps from a tens of Hz up to 0.48 kHz, while the central frequency can be selected from 0.72 to 1.81 kHz according to the volume ratio. The goal of this study is to serve as a database for the Primitive, Gyroid, Neovius, IWP, Diamond, Fischer–Koch S, and FRD TPMS structures for metamaterial designers.

三周期最小表面（TPMS）晶格结构具有轻质、高强度、能量吸收和波传播控制等优异性能，近年来得到广泛研究。然而，设计 TPMS 时的主要挑战之一是正确选择电池类型和体积比，以获得特定应用所需的特性。为此，这项工作对七种主要单元类型 TPMS 结构（包括 Primitive、Gyroid、Neovius、IWP、Diamond、Fischer-Koch S 和 FRD）在低于 2 kHz 频率范围内的带隙形成进行了全面的数值研究。以获得全面的体积比范围。结果表明，这七个 TPMS 结构在第三和第四色散曲线之间呈现出完整的带隙。带隙宽度很大程度上取决于 TPMS 晶格，并且当体积比超过 0.3 时，Neovius 和 Primitive 晶格上的带隙最宽（最大宽度分别为 0.458 kHz 和 0.483 kHz）。低于这个体积比，Primitive 结构的带隙可以忽略不计，Neovius 和 IWP 结构是 7 个测试的 TPMS 案例中的最佳候选。带隙的中心频率对晶格不太敏感，并且主要由体积比调整。通过这项研究，我们证明了周期性单元类型和体积比的正确选择可以将完整带隙的带宽调整为从几十赫兹到0.48 kHz，而中心频率可以根据需要在0.72到1.81 kHz之间选择。体积比。