Ultra-broad bandgap induced by hybrid hardening and softening nonlinearity in metastructure

Metamaterials are artificial microstructured media that exhibit unique effective material properties and can be tailored to achieve negative properties that inhibit the propagation of acoustic or elastic waves. However, the effectiveness of linear metamaterials (LMs) based on resonance mechanisms is limited to a narrow frequency band. To overcome this limitation, nonlinear metamaterials (NLMs) have been investigated for enlarged bandwidth and wave phenomena beyond the linear systems. This paper presents a new mechanism for achieving an ultra-broad bandgap using a chain of triplets of resonators, based on the combination of hardening-plus-softening nonlinearity. The paper begins by investigating the bandgap and transmission characteristics of NLMs with different arrangements of single-hardening or single-softening nonlinear spring element. Explicit expressions for the nonlinear dispersion relations have been derived through a perturbation method. The paper then explores the combination of hardening-plus-softening nonlinearity to achieve an ultra-broad bandgap, which is more than twice as wide as the bandgap in the corresponding LM. The transmission characteristics are investigated analytically and validated numerically, providing evidence for the existence and accuracy of the predicted ultra-broad bandgap. The paper also examines nonlinear phenomena such as the dual wavevector and inflection point of transmissions in detail. Finally, the physical origin of the ultra-broad bandgap is elaborated through the nonlinear frequency response of a unit cell solved using a high-order harmonic balance method. The findings of this study are expected to provide a new strategy for broadening vibration suppression and offer new insight into the behavior of nonlinear periodic structures.