Tunable Low-Frequency Bandgaps in Foldable Metamaterials based on MRE: Review and Numerical Analysis

Active control of low-frequency bandgaps remains a key challenge in vibration engineering. In foldable metamaterials, bandgap tuning is usually realized through geometric changes such as folding angle adjustment, which is slow and discrete. To overcome this limitation, we propose to replace the conventional springs in the resonators with magnetorheological elastomers (MREs), enabling continuous and fast bandgap control via external magnetic fields. A numerical study using the finite element method (FEM) is conducted to examine the dispersion relations and vibration transmission of the proposed structure. The results show that magnetic field strength and iron particle content can effectively shift the bandgap position and width. Supercell transmission analysis confirms that the theoretical bandgap predictions match well with the actual vibration attenuation. A hybrid supercell design further broadens the effective attenuation range. Besides, the work also offers a systematic background review of foldable metamaterials and active approaches, which provides a framework for designing actively tunable metamaterials for low-frequency vibration attenuation in applications such as precision instrument isolation and spacecraft micro-vibration control.