Summary The article presents an analysis of the dynamic behaviour of discrete flexural systems composed of Euler–Bernoulli beams. The canonical object of study is the discrete Green’s function, from which information regarding the dynamic response of the lattice under point loading by forces and moments can be obtained. Special attention is devoted to the interaction between flexural and torsional waves in a square lattice of Euler–Bernoulli beams, which is shown to yield a range of novel effects, including extreme dynamic anisotropy, asymmetric wave propagation, wave-guiding, filtering and the ability to create localised defect modes, all without the need for additional resonant elements or interfaces. The analytical study is complimented by numerical computations and finite element simulations, both of which are used to illustrate the effects predicted. A general algorithm is provided for constructing Green’s functions as well as defect modes. This algorithm allows the tuning of the lattice to produce pass bands, band gaps, resonant modes, wave-guides and defect modes, over any desired frequency range.

中文翻译：

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离散弯曲系统中的动态格林函数

总结 本文对由欧拉-伯努利梁组成的离散弯曲系统的动态行为进行了分析。研究的规范对象是离散格林函数，从中可以获得有关在力和力矩的点载荷下晶格的动态响应的信息。特别关注欧拉-伯努利梁的方格中弯曲波和扭转波之间的相互作用，这表明产生一系列新颖的效果，包括极端动态各向异性、不对称波传播、波导、滤波和能力创建局部缺陷模式，所有这些都不需要额外的谐振元件或接口。分析研究得到数值计算和有限元模拟的补充，两者都用于说明预测的效果。提供了用于构造格林函数以及缺陷模式的通用算法。该算法允许在任何所需频率范围内调整晶格以产生通带、带隙、谐振模式、波导和缺陷模式。