Finite-amplitude nonlinear waves in inertial amplification metamaterials: Theoretical and numerical analyses

The motivation of this study is to understand the unique characteristics of finite-amplitude elastic wave propagation in an inertial amplification (IA) system coupled with a Duffing resonator and leverage the unique opportunities offered by the IA mechanism and nonlinearities to achieve the modulation of elastic waves. Based on the assumption of the perturbation method, the effective range of the wave amplitude was investigated, which is usually ignored. Meanwhile, the obvious phenomenon of bandgap transition (between the single resonance bandgap and hybrid bandgap) is observed with varying IA levels. In particular, we demonstrated a new phenomenon of negative wave propagation and an obvious standing-wave mode in this system. Here, an analytical investigation of the amplitude-dependent and IA-dependent nonlinear dispersion is conducted based on the perturbation approach. Numerical simulations using the time-domain finite element method and Gaussian pulse excitation were performed to validate the nonlinear dispersion and negative motion of the wave packet. The research results can be used to tune wave propagation in metamaterials and provide ideas for the design of metamaterials, which can be used in practical circumstances for different energy transfer needs.