Design of a compliant locally resonant metamaterial unit cell for low-frequency vibration attenuation

Abstract

Vibrations have been studied in various engineering fields due to their detrimental and even destructive effects on structures. Suppressing low-frequency vibrations has been a research challenge for decades and is mostly achieved by implementing active vibration control techniques. In the last two decades, the emergence of locally resonant metamaterials has sparked the interest of several researchers to create passive vibration attenuation structures as an alternative to active vibration-suppressing techniques. This research focuses on developing a local resonator-based unit cell that is able to attenuate vibrations at a wide range of low frequencies. A literature research is performed on the state-of-the-art in the field of locally resonant metamaterials and their wave-suppressing properties. Several wave directions and types are considered,
while low-frequency vibration attenuating structures are actively discussed. A comparative study is done on current local resonator-based structures from which a novel compliant metamaterial is proposed that can suppress a wide range of low-frequency vibrations. The proposed novel compliant negative stiffness local resonator (NSLR) unit cell has the ability to attenuate low-frequency vibrations at a wide range of frequencies while exhibiting a large load-bearing capacity. This concept is based on compliant mechanisms and relies on the snap-through motion of buckled beams for its negative stiffness, whereas folded beams are used in the design as load-bearing positive stiffness components. The stiffness and load-bearing capacity of the unit cell is determined by analytical and FEM-based numerical models, while dispersion relations and transmissibility functions are used to identify the dynamic vibration attenuation behavior. A prototype is produced by FDM additive manufacturing and tested in an experimental setup to verify the load-bearing capacity. An analytical and numerical load-bearing capacity between 100 N and 102 N, and 111 N to 115 are established, respectively, with an effective vibration
attenuation displacement range of 2.5 mm. The FEM simulated band gap of a single unit cell ranges from 6.0 Hz to 64.8 Hz, while the analytical model shows a band gap from 9.6 Hz to 59.5 Hz. The manufactured NSLR prototype features parasitic resonator rotations, requiring additional stiffness constraints to test its vibration attenuation properties in practice. These analyses show the promising capabilities of the NSLR unit cell as a building block in metamaterials to protect
structures from low-frequency vibrations at a wide range.