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.

非线性周期结构可以呈现丰富的非线性波物理。由于双稳态周期结构中的多重平衡，由周期双稳态振荡器组成的模型（即双稳态周期结构）与那些由单稳态振荡器组成的非线性周期系统有着本质的区别。尽管受到广泛关注，但双稳态周期结构中谐波和冲击波传播的特性，尤其是规律性背后的随机性和可调性，尚未得到充分理解。本文报告基于数值方法的答案。我们考虑了带隙、振动中心、波幅和传输的变化趋势，并展示了它们对能量传输的影响。我们发现快速通过行为总是呈现局部内在随机性和整体规律性，也就是说，它不会按顺序发生。对于谐波和冲击波，大部分能量都集中在快速通过振荡器内部，这改变了能量传输的规律，对冲击波保护很有意义。双稳态周期结构可以通过将波幅调整到临界值来将带隙的初始频率移动到接近零，从而呈现极低频和宽带波衰减，从而提供动态可调性。冲击脉冲的阻尼和强度对冲击波的传播有显着影响。该工作为用于弹性波衰减和冲击波防护的双稳态周期结构的设计和应用提供了指导。大多数能量都集中在快速通过振荡器内部，它改变了能量传输的规律，对冲击波保护很有意义。双稳态周期结构可以通过将波幅调整到临界值来将带隙的初始频率移动到接近零，从而呈现极低频和宽带波衰减，从而提供动态可调性。冲击脉冲的阻尼和强度对冲击波的传播有显着影响。该工作为用于弹性波衰减和冲击波防护的双稳态周期结构的设计和应用提供了指导。大多数能量都集中在快速通过振荡器内部，它改变了能量传输的规律，对冲击波保护很有意义。双稳态周期结构可以通过将波幅调整到临界值来将带隙的初始频率移动到接近零，从而呈现极低频和宽带波衰减，从而提供动态可调性。冲击脉冲的阻尼和强度对冲击波的传播有显着影响。该工作为用于弹性波衰减和冲击波防护的双稳态周期结构的设计和应用提供了指导。双稳态周期结构可以通过将波幅调整到临界值来将带隙的初始频率移动到接近零，从而呈现极低频和宽带波衰减，从而提供动态可调性。冲击脉冲的阻尼和强度对冲击波的传播有显着影响。该工作为用于弹性波衰减和冲击波防护的双稳态周期结构的设计和应用提供了指导。双稳态周期结构可以通过将波幅调整到临界值来将带隙的初始频率移动到接近零，从而呈现极低频和宽带波衰减，从而提供动态可调性。冲击脉冲的阻尼和强度对冲击波的传播有显着影响。该工作为用于弹性波衰减和冲击波防护的双稳态周期结构的设计和应用提供了指导。