SUMMARY

Wave propagation in periodic structures has attracted the interest of the engineering community due to the presence of bandgaps, or forbidden frequency ranges of propagation, which have inspired devices to include filters, diodes, switches, and waveguides. Geometric and material nonlinearities present in periodic structures result in propagation features (e.g., direction, cut-off/cut-on frequencies, group velocity) dependent on wave amplitude, thereby providing an additional means to manipulate wave propagation. This work explores waveform invariance, stability, and nonreciprocity as enabled by nonlinear periodic structures. One-dimensional and two-dimensional discrete lattices are considered. Waveform invariance, in which a multi-harmonic solution persists without dispersing for all space and time, and plane wave stability, in which high amplitude waves undergo significant distortion of their spectral content, are informed by perturbation analysis of the lattices’ equations of motion. Nonreciprocity exploits a preferred energy transfer that occurs from large to small scales, coupled by strongly nonlinear springs, to create a periodic lattice with highly asymmetrical wave propagation. The proposed work will also explore internal resonance: waves with specific harmonic content undergo strong energy transfer between their spectral amplitudes. Theoretical findings are confirmed with numerical simulations and the proposed work includes experimental validation. Such findings may apply to damage detection, data encryption, and shock and vibration mitigation.