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On the unwrapping of dispersion curves in the irreducible Brillouin zone by means of a spatial Fourier transform approach

Journal Contribution - Journal Article

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, focusing 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.
Journal: International Journal of Solids and Structures
ISSN: 0020-7683
Volume: 196
Pages: 67 - 75
Number of pages: 9
Publication year:2020