A nonlinear acoustic metamaterial beam with tunable flexural wave band gaps

Abstract

Although linear acoustic metamaterials (LAMs) have been widely studied, the design and analyses of nonlinear acoustic metamaterials (NAMs) are relatively immature. In this paper, a new NAM beam is designed, which is composed of a homogeneous beam with periodic resonant units attached on its top surface. Each resonant unit consists of two Duffing oscillators connected in series. First, an analytical model is developed based on the harmonic balance method, from which the amplitude-frequency response and dispersion of flexural wave are derived, and the position and width of the band gaps produced by this novel structure are quantitatively evaluated. Then, the effects of the linear and nonlinear stiffness, as well as the arrangement of the series-connected resonators on the frequency band structure are discussed. A finite element (FE) simulation is conducted to obtain the transmission of a finite NAM beam. The numerical results show that the frequency range of vibration suppression is consistent with the analytically predicted band gap, which validate the developed analytical model. Our study demonstrates that comparing with the corresponding linear counterpart, the system nonlinearity effectively enhances the tunability of the band gap of the flexural wave. It’s worth mentioning that an ultra-wide band gap starting from 0Hz can be achieved via introducing softening nonlinearity, which is quite attractive in engineering applications requiring low-frequency vibration suppression.