A Novel Auxetic Trampoline Metamaterial With Low‐Frequency Bandgap Tunability Under Prestrain

External mechanical loadings can change the bandgap of phononic metamaterials by altering their structure or material properties. However, traditional trampoline metamaterials are typically loaded in one or two dimensions. The potential to adjust the bandgap by loading in three dimensions is still in the early stages. This study proposes a trampoline metamaterial with a negative Poisson's ratio (TM‐N), which adjusts the bandgap through small deformations under three‐dimensional loading. The dispersion curves of TM‐N and TM‐P are compared using mass‐spring models and finite element (FE) simulations. Compared to TM‐N, TM‐P shows an opposite trend in the bandgap when the substrate is compressed. The adjustable performance of the TM‐N bandgap under prestress is also discussed. Numerical results show that increasing the strain ratio χ expands the bandgap and increases its bandwidth. The effects of cylinder perforated ellipticity and substrate thickness T on the bandgap are analyzed. With χ = −2, = 4, and T = 5.5 mm, the minimum starting frequency of the bandgap is 134.5 Hz, and the relative bandwidth is 86%. The proposed TM‐N effectively reduces the bandgap frequency and widens the bandgap range under three‐dimensional loading, offering new possibilities for real‐time bandgap adjustment.