Design and additive manufacturing of elastic metamaterials with 3D lever-type inertial amplification mechanisms for mitigation of low-frequency vibration

Abstract

This paper proposes a three-dimensional lever-type inertial amplification metamaterial for the mitigation of low-frequency vibration. This metamaterial was developed as a small, stiff, and single-phase structure that can inhibit the transmission of vibration in a certain frequency range below 100 Hz. An analytical model was developed to derive analytical solutions for the resonance and anti-resonance frequencies of the metamaterial unit cell. A dispersion equation was also derived to investigate the vibration transmissibility of the periodic structure. Finite element analysis was performed to obtain the frequency response of the unit cell and periodic structures. The analytical solutions were then verified through comparisons with the results of the finite element analysis. The proposed metamaterial was fabricated via selective laser sintering of a thermoplastic resin, and experiments were performed to measure the vibration transmissibility of the unit cell loaded with a mass and that of the periodic structures. A unit cell with a diameter of 100 mm and height of 65.8 mm showed low transmissibility in a wide frequency range around the anti-resonance frequency at 80 Hz while supporting up to 9.45 kg mass.