Periodic structures usually present a frequency response spectrum with regions characterized by large modal spacing (big distance between two resonance peaks) and low vibrating responses. Such regions are called band gaps, and they can be generated either by the Bragg scattering or by the local resonance mechanisms, where the vibrating waves are attenuated and do not propagate along the structure. It has been shown in the literature that corrugated beams (beams shaped in a periodic geometry) are not an exception, and they do present band gaps. It was observed that the band gap central frequency and its bandwidth depend on the number and height of bumps of the beam. Hence, the geometry of the beam defines the resultant band gap region in its frequency spectrum. In this work, one investigates the effect of “summing” two periodic corrugated beams in terms of their spatial Fourier content. It is shown that, by adopting a geometry composed of spatial Fourier components from two other corrugated beams, the beam preserves the band gaps of the original ones. This is verified both numerically and experimentally. The plane wave expansion method is used to obtain the dispersion diagrams, whereas conventional modal analysis is employed to obtain the experimental frequency response functions of the original and “summed” beams.

中文翻译：

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波纹梁的空间傅里叶求和及其带隙形成

周期性结构通常呈现出频率响应谱，其特征在于大模态间距（两个共振峰之间的距离大）和低振动响应的区域。这些区域称为带隙，它们可以通过布拉格散射或局部共振机制产生，其中振动波被衰减并且不沿着结构传播。文献表明，波纹梁（周期性几何形状的梁）也不例外，它们确实存在带隙。据观察，带隙中心频率及其带宽取决于梁凸块的数量和高度。因此，光束的几何形状定义了其频谱中的最终带隙区域。在这项工作中，研究人员研究了“求和”两个周期性波纹梁的空间傅立叶内容的效果。结果表明，通过采用由另外两个波纹梁的空间傅立叶分量组成的几何形状，该梁保留了原始波纹梁的带隙。这已通过数值和实验得到验证。平面波展开方法用于获得色散图，而传统模态分析用于获得原始光束和“求和”光束的实验频率响应函数。