Origami-based mechanical metamaterials and metastructure have been demonstrated to exhibit unique properties originating from their intricate geometries of folding. This research aims to extend the current investigation level from quasi-statics to dynamics. In detail, this research focuses on the wave dynamics of a metastructure composed of stacked Miura-ori (SMO) units. The SMO unit could possess two stable configurations, endowing the metastructure with rich possibilities in the layout of its periodic repeating cell. Through linear dispersion analyses and numerical studies, we show that the long-desired stopband tunability and programmability of the metastructure along the three principal directions can be acquired by strategically program the layout of the periodic cell. Based upon that, we further discover that energy supratransmission through the metastructure is possible within the stopband by increasing the driving amplitude. Through numerical means, the amplitude threshold of supratransmission is obtained. We demonstrate that the fundamental mechanism that triggers the supratransmission phenomenon is the transition of the responses from the low energy intrawell oscillations to the high energy interwell oscillations. Numerical studies also indicate that the supratransmission threshold can be effectively tailored by adjusting the periodic cell layout. The results of this research provide a wealth of fundamental insights into the origami wave dynamics and offer useful guidelines for developing origami metastructures with tunable and programmable dynamic characteristics.

中文翻译：

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堆叠Miura-origami元结构中的可编程阻带和超传输效应

基于折纸的机械超材料和元结构已展示出源自其复杂的折叠几何形状的独特属性。这项研究旨在将当前的研究水平从准静态扩展到动态。详细地，本研究集中于由堆叠的Miura-ori（SMO）单元组成的元结构的波动力学。SMO单元可以具有两个稳定的配置，在其周期性重复单元的布局中赋予元结构以丰富的可能性。通过线性色散分析和数值研究，我们表明，通过策略性地编程周期单元的布局，可以获得沿三个主要方向的元结构的长期期望的阻带可调性和可编程性。基于此，我们进一步发现，通过增加驱动幅度，可以在阻带内通过超结构传输能量。通过数值手段，获得超透射的幅度阈值。我们证明了触发超传输现象的基本机制是响应从低能井内振荡过渡到高能井内振荡。数值研究还表明，可以通过调整周期性的细胞布局有效地调整超透射阈值。这项研究的结果为折纸波动力学提供了丰富的基础知识，并为开发具有可调和可编程动态特征的折纸元结构提供了有用的指导。