Wave directionality in periodic lattice structures
Abstract
We discuss the wave directionality for in-plane and out-of-plane waves in three-dimensional selfsimilar
and non-self-similar square periodic lattices. The lattices studied are square lattice, square
in the square hierarchical lattice, and hexagon in a square hierarchical lattice. Finite Element
Analysis is used to calculate dispersion relations and directionality properties for these lattice
structures following a 25/25 grid covering the complete Brillouin zone. The investigation is
performed by combining the Floquet-Bloch theory of periodic structures with the commercial FE
solver, Comsol Multiphysics. A method to distinguish between the in-plane and out-of-plane wave
modes is explained in detail. Multiple surfaces are selected to show that the dispersion surfaces
overlap in frequency and beaming direction; thus, requiring an efficient way to distinguish the inplane
and out-of-plane modes. The effects of the hierarchy on the wave beaming in the chosen
lattices are studied. The in-plane waves are observed to beam mostly along 0° and 90° directions
in the square lattice, while a more equal spread is observed for the hierarchical lattices. Significant
beaming is observed in the hexagon in the square lattice for the out-of-plane waves. The effect of
hierarchy on the generation of bandgaps is studied. Compared with a non-hierarchical square
lattice, the hierarchical lattice structures display significantly lowered group velocity magnitudes.
The non-self-similar hierarchical lattice was found to provide bandgaps at lower frequencies and
slower group velocities as compared to the self-similar hierarchical lattice.
Description
Thesis (M.S.)-- Wichita State University, College of Engineering, Dept. of Aerospace Engineering