Multiscale frequency conversion through input-independent dynamics of bistable lattices

In this study, we extend the input-independent dynamics to higher-dimensional metastructures. A metabeam is constructed by integrating a bistable lattice along a beam-like outer frame. We obtain frequency response diagrams showing output frequency spectra for each input frequency and observe nonlinear out-of-plane behavior as long as transition waves are triggered along the in-plane bistable lattice direction. Similar to the observations in its one-dimensional counterpart, the transverse output frequencies remain coherent around a single dominant frequency regardless of the input frequency that triggers the transition waves. This result shows transfer of energy between two different length scales – localized in-plane waves and global out-of-plane deflections – and implies that such metabeams display efficient multiscale frequency conversion. Also identified is two qualitatively different routes to frequency conversion depending on the discreteness of the bistable lattice, enabling a greater design freedom. Furthermore, the unit cell design can be easily tuned to alter the metabeam properties, especially in terms of the operating frequency range and output frequency, allowing for a broad range of engineering applications.