Vibration properties and optimized design of a nonlinear acoustic metamaterial beam

Lightweight, low-frequency, broadband and highly efficient vibration reduction is widely desired in various devices. Nonlinear acoustic metamaterial (NAM) is a new type of metamaterial that may possess these vibration reduction features. However, the laws governing the manipulation of the NAM vibration response and its optimized design have not been addressed. This paper numerically and experimentally studies the manipulation laws and optimized design of the NAM beam reported in [Nature Comm., 8: 1288(2017)]. The strongly nonlinear metacell consists of three bridging-coupled resonators: A Duffing oscillator, a flexural resonator and a vibro-impact resonator. Both time-domain and frequency-domain finite element models are established to calculate the vibrations of the beam. We systematically study the influences of the amplitude, nonlinear stiffness coefficients, resonance frequencies, mass and beam thickness on the bandwidth and efficiency of its vibration reduction properties. Moreover, based on these laws, we present an optimized lightweight NAM beam to realize the low-frequency, broadband and highly efficient vibration reduction with the greatly reduced attached mass. Finally, different NAM samples are fabricated to verify the efficient reduction effect. This work could support the study, creation and application of NAMs in the future.