In this paper, shape transformers, a set of non-dimensional geometrical parameters that define beam cross-section efficiencies based on their size and shape, are employed in the wave propagation analysis of two-dimensional periodic lattice structures. Here, shape transformers of lattice unit-cell beams are used as design variables to tailor the frequency band gaps of the lattice structure, in the form of their mid frequencies and aspect ratios, by means of numerical Bloch-periodic simulation. Case studies are presented for lattices with square and hexagon Bravais symmetries where a total of six different unit-cell topologies are studied, considering 12 classes of different cross-section shapes. It is observed that a significant shift of the waveband branches towards lower frequencies are obtained with the variation of shape transformers from a void to a filled envelope configuration. Moreover, while changing the cross-section geometric variables, it is possible to determine associated values of maximum aspect ratios of band gap frequencies, thus identifying cross-section shapes that have better performance with respect to lattice dynamic characteristic. It is also found that the “H” and “I” cross-section shapes, in comparison to other shape families presented, resulted in the maximization of the band gap aspect ratio while maintaining a low frequency range, hence being ideal candidates for designing lattice metamaterials with lower frequency ranges of elastic wave attenuation. Furthermore, among all lattice topologies investigated, it is noted that the employment of diamond cross-section and its derivatives resulted in the greatest sensitivity of the mid-frequency shift of the band gap with respect to variations in cross-section geometric efficiency. It is also observed, as a general behavior for all unit-cells studied, that when scaling up the in-plane height of the cross-section, the aspect ratio of the band gap was maximized. Finally, using the Modal Assurance Criterion, we demonstrated that the variation in the shape transformers conserves the consistency between the eigenwaves of unit-cells at different characteristic points of the Irreducible Brillouin Zone. The presented study paves the way for the development and the systematic implementation of a novel wave attenuation tuning technique.

在本文中，形状变换器是二维无定形几何参数的集合，该参数根据其大小和形状定义了梁的横截面效率，被用于二维周期性晶格结构的波传播分析中。在此，通过数值布洛赫-周期模拟，将晶格单位晶格光束的形状变换器用作设计变量，以其中频和纵横比的形式调整晶格结构的频带间隙。针对具有方形和六边形Bravais对称性的晶格进行了案例研究，其中考虑了12类不同的横截面形状，总共研究了六种不同的晶胞拓扑。观察到，随着形状变换器从空隙到填充的包络线结构的变化，获得了频带分支朝着较低频率的显着偏移。此外，在改变横截面几何变量的同时，可以确定带隙频率的最大纵横比的相关值，从而识别出相对于晶格动力学特性具有更好性能的横截面形状。还发现，与呈现的其他形状系列相比，“ H”和“ I”形截面形状导致带隙纵横比最大化，同时保持低频范围，因此是设计晶格的理想候选者弹性波衰减频率范围较低的超材料。此外，在所有之中 此外，在改变横截面几何变量的同时，可以确定带隙频率的最大纵横比的相关值，从而识别出相对于晶格动力学特性具有更好性能的横截面形状。还发现，与呈现的其他形状系列相比，“ H”和“ I”形截面形状导致带隙纵横比最大化，同时保持低频范围，因此是设计晶格的理想候选者弹性波衰减频率范围较低的超材料。此外，在所有之中 此外，在改变横截面几何变量的同时，可以确定带隙频率的最大纵横比的相关值，从而识别出相对于晶格动力学特性具有更好性能的横截面形状。还发现，与呈现的其他形状系列相比，“ H”和“ I”形截面形状导致带隙纵横比最大化，同时保持低频范围，因此是设计晶格的理想候选者弹性波衰减频率范围较低的超材料。此外，在所有之中 因此，可以确定相对于晶格动力学特性具有更好性能的横截面形状。还发现，与呈现的其他形状系列相比，“ H”和“ I”形截面形状导致带隙纵横比最大化，同时保持低频范围，因此是设计晶格的理想候选者弹性波衰减频率范围较低的超材料。此外，在所有之中 因此，可以确定相对于晶格动力学特性具有更好性能的横截面形状。还发现，与呈现的其他形状系列相比，“ H”和“ I”形截面形状导致带隙纵横比最大化，同时保持低频范围，因此是设计晶格的理想候选者弹性波衰减频率范围较低的超材料。此外，在所有之中在研究晶格拓扑时，要注意的是，采用金刚石横截面及其派生法对带隙的中频偏移相对于横截面几何效率的变化具有最大的敏感性。还观察到，作为所研究的所有单元电池的一般行为，当按比例增大横截面的平面内高度时，带隙的纵横比被最大化。最后，使用模态保证标准，我们证明了形状变换器的变化可以在不可约布里渊区的不同特征点上保持单位单元本征波之间的一致性。提出的研究为新型波衰减调谐技术的开发和系统实现铺平了道路。