Abstract Using Bloch–Floquet boundary conditions implies a periodicity in both the spatial and wavenumber domains, causing the numerically computed wavenumbers to be folded or aliased within the Brillouin zone. A methodology is presented to unwrap the wavenumber spectrum to extended Brillouin zones using a Fourier transform method in the spatial domain, thus providing new insights on the physical meaning and relative amplitudes of aliased wave components. In addition, a procedure is presented to identify out-of-plane (Lamb wave type) components, which are usually of interest for thin structures. The proposed methodologies were applied to finite element based simulations of a 2D periodic reticulated structure consisting of interconnected rectangular struts with orthorombic symmetry. This reticulated structure was used as a toy model for the skeleton in porous media, focussing on the out-of-plane waves. Laser ultrasonic experiments were conducted to verify the numerical results. Both the simulations and measurement results indicate that, in spite of bandgap features induced by the periodicity of the structure, the dispersion behavior of the out of plane Lamb wave modes in the considered type of structure is similar to the one of the Lamb waves of a homogeneous plate with thickness equal to the one of the struts, both for wavenumbers within and outside the Irreducible Brillouin Zone.

中文翻译：

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利用空间傅里叶变换方法展开不可约布里渊区中的色散曲线。

摘要 使用 Bloch-Floquet 边界条件意味着空间域和波数域中的周期性，导致数值计算的波数在布里渊带内折叠或混叠。提出了一种在空间域中使用傅立叶变换方法将波数谱展开到扩展布里渊区的方法，从而提供了对混叠波分量的物理意义和相对幅度的新见解。此外，还介绍了识别平面外（兰姆波型）分量的程序，这些分量通常对薄结构感兴趣。所提出的方法应用于基于有限元的二维周期性网状结构的模拟，该结构由具有正交对称性的互连矩形支柱组成。这种网状结构被用作多孔介质中骨架的玩具模型，专注于平面外波。进行了激光超声实验以验证数值结果。模拟和测量结果都表明，尽管结构的周期性引起了带隙特征，但在所考虑的结构类型中平面外兰姆波模式的色散行为类似于 a 的兰姆波之一。对于不可约布里渊区内外的波数，均质板的厚度等于其中一个支柱的厚度。