离散弯曲系统的动态格林函数
Dynamic Green's functions in discrete flexural systems
摘要：
本文分析了由欧拉-伯努利梁组成的离散弯曲系统的动力特性。规范的研究对象是离散的格林函数，从中可以获得关于力和力矩的点载荷下的晶格的动态响应的信息。特别注意的是致力于弯曲和扭转波之间的相互作用，在一个正方形网格的欧拉-伯努利梁，这是产生一系列的新的效果，包括极端的动态各向异性，非互易性，波导，过滤，并能够创建本地化的缺陷模式，所有不需要额外的谐振元件或接口。数值计算和有限元模拟，这两者都被用来说明预测的效果的分析研究补充。给出了构造格林函数和缺陷模的一般算法。该算法允许晶格的调谐以在任何期望的频率范围内产生通带、带隙、谐振模式、波导和缺陷模式。
英文摘要：
The paper 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, non-reciprocity, 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.
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