Interband targeted energy transfer, wave arrest, and redirection in phononic lattices with strongly nonlinear local resonators

Intentionally introducing nonlinearity into phononic metamaterials has facilitated the development of novel passive elastoacoustic devices (e.g., diodes and nonlinear waveguides). The performance of these devices is primarily governed by the capability of the metamaterial to achieve intermodal targeted energy transfer. In this study, we explore phononic metamaterials with strongly nonlinear local resonators that are capable of significant interband targeted energy transfer (IBTET), that is, of nonlinear energy scattering from a primary, high-energetic pass band containing the energy of external excitation to higher- or lower-frequency secondary bands. The nonlinearity arises from pronounced geometric effects, specifically from the inclusion of local (internal) resonators with inclined linear stiffnesses. This geometric arrangement can exhibit characteristics such as softening-hardening nonlinearity and bistability, contingent upon the initial angle of inclination where the local resonator is at equilibrium. We conducted numerical simulations on a one-dimensional (1D) semi-infinite phononic lattice (modeled as a 1D lattice composed of a large number of coupled oscillators, possessing free boundaries) with varied distributions of nonlinearity and different initial angles of inclination of the internal resonators. The results demonstrate that the system exhibits robust IBTET at specific wave amplitudes. Furthermore, we show that strong nonlinearity can profoundly influence the bandgap topology under specific parameters. This band alteration can induce wave arrest and localization within the nonlinear phononic lattice and give rise to phenomena such as negative group velocity and break of acoustic reciprocity. To provide quantitative measures for the efficacy of the nonlinear phononic lattice for IBTET and wave manipulation, we quantify the induced nonlinear energy scattering across different bands using a wavelet-based technique, which on broader context, is valid for decomposition of multiscale acoustics in general classes of acoustic waveguide. Potential applications are discussed.