Aperiodic metamaterials can host topological or localized wave modes, and gradually changing structures are known to induce conversion between elastic wave types. This work describes a family of one dimensional, aperiodic elastic structures that can host localized modes or achieve low-frequency attenuation by varying a single geometrical parameter, i.e., the ratio between the sizes of two interacting periodic structures. Two periodic sets of slits on the top and bottom of a slender beam scatter bending waves. The thickness profile and cross section of beams with a period ratio close to 1 varies slowly, resulting in localized wave modes. The localization happens because of spatially confined band gaps and is only triggered for certain excitation locations, unlike wave localization due to a local defect. If the periods differ more, broad band gaps appear at wave numbers equal to linear combinations of the individual Brillouin zone edges of each set of slits. We call these interaction band gaps, since they result from the interplay between two periodic sets of slits. Low-frequency wave attenuation is achieved while maintaining a high overall bending stiffness.

中文翻译：

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准周期光束中的弯曲波定位和相互作用带隙

非周期性超材料可以容纳拓扑或局部波模式，并且逐渐变化的结构已知会引起弹性波类型之间的转换。这项工作描述了一个一维非周期性弹性结构家族，可以通过改变单个几何参数（即两个相互作用的周期性结构的大小之比）来承载局部模式或实现低频衰减。细长光束的顶部和底部的两组周期性缝隙会散射弯曲波。周期比接近1的光束的厚度分布和横截面变化缓慢，从而导致局部波模。定位是由于空间限制的带隙而发生的，并且仅针对某些激发位置才触发，这与由于局部缺陷而引起的波定位不同。如果期间相差更大，宽带隙出现在波数等于每组狭缝的单个布里渊区边缘的线性组合的情况下。我们将这些相互作用带隙称为“相互作用带隙”，因为它们是由两个周期性缝隙之间的相互作用产生的。在保持高整体弯曲刚度的同时，实现了低频波衰减。