Harmonic and shock wave propagation in bistable periodic structure: Regularity, randomness, and tunability

Nonlinear periodic structures can present abundant nonlinear wave physics. The model consisting of periodic bistable oscillators (i.e., the bistable periodic structure) is essentially different from those nonlinear periodic systems consisting of monostable oscillators due to multiple equilibria in bistable periodic structure. Despite the extensive attention received, properties of harmonic and shock wave propagation in bistable periodic structure, especially the randomness and tunability behind regularity, have not been fully understood. This article reports the answers based on numerical method. We consider the varying trends of the band gap, vibration center, wave amplitude, and transmission and show their effects on energy transport. We find that the snap-through behavior always presents local intrinsic randomness with the regularity in whole, that is, it does not happen in sequence. For both harmonic and shock wave, most energy is localized inside the snap-through oscillators that changes the regularity for energy transport and is meaningful for shock wave protection. Bistable periodic structure can present very low-frequency and broadband wave attenuation by shifting the initial frequency of the band gap to nearly zero through tuning the wave amplitude to a critical value, which offers dynamic tunability. The damping and intensity of the shock pulse have significant effects on the shock wave propagation. This work provides guidance for the design and application of bistable periodic structure for elastic wave attenuation and shock wave protection.