Programmable quasi-zero-stiffness mechanical metamaterials based on deep learning and multi-level assembly

Mechanical metamaterials, characterized by their exceptional physical properties derived from precise structural design, have emerged as promising candidates for low frequency vibration isolation. However, traditional vibration control methods often encounter difficulties in effectively suppressing ultra-low frequency vibrations due to limitations in space and mass. To address these limitations, we propose a data-driven inverse design framework for programmable quasi-zero-stiffness (QZS) mechanical metamaterials, wherein deep learning models are utilized to custom-design the geometry of curved-beam structures according to specific performance requirements. When integrated with a multi-level assembly strategy, this approach enables the creation of metamaterials exhibiting multiple QZS operational ranges. The designed metamaterials display a staircase-like force–displacement curve, demonstrating several QZS regions that enable efficient vibration isolation across a wide frequency range. Finite element analyses and quasi-static compression experiments confirm a staircase force–displacement response with multiple QZS regimes, and representative assembled structures achieve an amplification of platform height of about 36 while maintaining a maximum principal strain of about 3%. Vibration tests further show that, under QZS-matched loading conditions, the transmittance remains below 0 dB over most of the tested 0–64 Hz frequency range, except for a narrow resonance peak near approximately 4 Hz. The proposed framework offers a scalable route to compact, programmable, multi-platform QZS metamaterials for broadband low frequency vibration isolation in applications such as aerospace structures and vehicle seats.