Analytical modeling and 3D printing of locally resonant composite sandwich metamaterials with inertial amplification mechanisms

Abstract

In this paper, a locally resonant sandwich metamaterial beam with inertial amplification mechanisms is presented for flexural vibration attenuation. This sandwich metamaterial is proposed as a lightweight structure with a low-frequency stopband. An analytical model was developed to derive the equations of motion for the resonator core and skin plate using Hamilton’s principle. Analytical solutions for the stopband boundary frequencies were derived from the equations of motion. The analytical solutions demonstrated that inertial amplification resonators can exhibit lower resonance frequencies than linear spring-mass resonators with the same weight and spring constant. It was also shown that the proposed sandwich beam exhibited a lower frequency stopband in exchange for the stopband width. Finite element method analyses and experiments were performed to investigate the frequency response of the sandwich beam. The flexural vibration of the sandwich beam was significantly attenuated within a certain frequency range. The frequency range with low transmissibility agreed well with the stopband predicted by the analytical solutions.