A novel approach to metamaterial design is introduced through the development of a stable 3D woodpile structure composed of slender cylindrical beams. These beam elements possess diverse bending vibration modes, intricately coupled with propagating waves, leading to complex wave dynamics within the structure. For the efficient analysis of various architectures, an extended discrete element model (DEM) is introduced to accurately emulate the local resonance caused by the beam’s bending vibration modes. The high level of accuracy achieved by the DEM is attributed to the utilization of a physics-informed discrete element modeling approach, rooted in continuum beam theory and wave dynamics within periodic structures. Utilizing the extended DEM, the interplay between propagating waves and local resonance within the beams is investigated, and the adjustability of mode coupling is confirmed by altering the interacting positions of neighboring beams. Subsequent to this, a graded 3D woodpile architecture is designed to progressively superimpose multiple frequency band structures. By adjusting mode coupling, it is shown that the graded woodpile is capable of displaying either a broad frequency passband or a broad frequency bandgap. Further demonstration reveals that the broad frequency bandgap facilitates high-frequency filtering, which effectively attenuates impact waves without the need for additional damping. The stable 3D woodpile architecture proposed in this study shows great potential for practical applications in vibration filtering and impact mitigation across various domains, ranging from small-scale material design to large-scale constructions.

中文翻译：

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通过振动模式耦合在 3D 木桩建筑中雕刻波传播


通过开发由细长圆柱梁组成的稳定 3D 木桩结构，引入了一种新的超材料设计方法。这些梁元件具有不同的弯曲振动模式，与传播波错综复杂地耦合，导致结构内产生复杂的波动力学。为了有效地分析各种架构，引入了扩展离散元模型 （DEM） 来精确模拟由梁的弯曲振动模式引起的局部共振。DEM 实现的高精度归功于利用了基于物理信息的离散元建模方法，该方法植根于周期性结构内的连续梁理论和波动力学。利用扩展的 DEM，研究了波束内传播波和局部共振之间的相互作用，并通过改变相邻波束的相互作用位置来确认模式耦合的可调性。在此之后，设计了渐变的 3D 木桩架构，以逐步叠加多个频段结构。通过调整模式耦合，表明分级木桩能够显示较宽的频通带或较宽的频隙。进一步的演示表明，宽频带隙有助于高频滤波，从而有效地衰减冲击波，而无需额外的阻尼。本研究提出的稳定 3D 木桩结构在从小规模材料设计到大规模建筑的各个领域的振动过滤和冲击缓解方面显示出巨大的实际应用潜力。