Elastic wave propagation through 3-dimensional cubic lattice structures

Abstract

In this study, the elastic wave propagation in 3-dimensional periodic lattice structure was investigated. The investigation was performed on the three cubic lattice structures (Simple Cubic, Body Centered Cubic, and Face Centered Cubic) and the Octet-truss lattice structure due to its recorded exemplary mechanical properties. The Finite Element Analysis tool COMSOL Multiphysics was employed in obtaining the planar dispersion property relating the eigen-frequencies along the wave vector path defined by the symmetry points of the Irreducible Brillouin Zone. From the dispersion curve, it was shown that there exist frequency regions with no solutions to the wave equation, and thus represents a stop zone for wave propagation. Various stop zones termed band gaps were identified intuitively from observing the dispersion relations. These band gaps are namely the total band gaps spanning along the entire wave vector path and partial band gaps which is limited to a wave direction. It was observed that there exist band gaps classified as caused by the structural resonance of a set of struts in the selected lattice structure. Also, wave selective band gaps termed polarized band gaps were identified by a careful study of the mode shapes enabling the classification of the individual dispersion bands to a wave type (longitudinal, flexural, or torsional). Borrowing a leaf from the concept of elastic metamaterials, the effect of changing the lattice structure's standard topology by including locally resonant sub-structures was also analyzed. It was shown that these sub-structures create a local resonant band gap at the tuned frequency which is always bounded by a flat dispersion band on the lower end of the stop zone.