Deep-squat inspired flexible metastructure for low-frequency vibration attenuation via stiffness regulation

Developing metamaterials with programmable bandgap tunability is a critical challenge for adaptive low-frequency vibration control. Purely passive curved beams lack real-time tunability, while purely active electromagnetic systems lack initial bandgaps and face power constraints. Inspired by human biomechanics, this paper proposes a variable-stiffness metamaterial integrating active and passive mechanisms. This design synergistically combines flexible beams for passive stiffness regulation and an electromagnetic structure for active modulation into a single unit cell. Passive pre-compression establishes the baseline stiffness and initial bandgap frequency. Under this state, the electromagnetic structure facilitates wide-range, dynamic fine-tuning of the bandgap by modulating positive and negative stiffness. Crucially, varying the input current yields a significantly faster tuning response than mechanically altering beam compression. System statics, modeled via the discrete beam constraint model and filament method, are validated by compression tests. Results demonstrate that under a 10 mm pre-compression, adjusting the input current alone yields a 3.15-fold variation in stiffness (ranging from 0.543 N/mm to 1.711 N/mm). Furthermore, band structure and transmissibility are theoretically modeled using dynamic analysis and the Galerkin method, with vibration isolation experiments confirming the metamaterial's excellent performance. This active-passive synergistic strategy overcomes the bottlenecks of single-mode tuning, achieving a broader stiffness range and faster response speeds. This work provides a novel paradigm for designing programmable smart metamaterials, demonstrating broad prospects for low-frequency vibration suppression in medical equipment, precision instruments, and engineering structures.