Nonlinear Tunability of Elastic Waves in One-Dimensional Mass-Spring Lattices Attached with Local Resonators

Vibration propagates in the form of elastic waves. The tuning of elastic waves is of great significance for vibration and noise reduction. The elastic metamaterials (EMs), which can effectively prohibit elastic wave propagation in the band gap frequency range, have been widely studied. However, once the structures of the EMs are determined, the band gap is also determined. In this paper, a discrete nonlinear elastic metamaterial is proposed. The harmonic balance method is used to derive the nonlinear dispersion relation combined with Bloch’s theorem. The low frequency band gap near the linear natural frequency of local resonators is obtained. The theoretical results show that the nonlinearity will change the starting and ending frequencies of the band gap. In addition, amplitude can also influence the band gap. This means that the amplitude can be changed to achieve the tunability of elastic waves in nonlinear elastic metamaterials. Finally, the theoretical results are verified by numerical simulation, and the results are in good agreement with each other.