Genetic Programming-based Phononic Bandgap Structure Design

Report No. ARL-TR-5733
Authors: Raymond A. Wildman and George A. Gazonas
Date/Pages: September 2011; 36 pages
Abstract: Two-dimensional phononic bandgap materials are designed using a genetic programming topology optimization method and a finite element elastic wave solver. The optimization problem involves maximizing the bandgap, or range of blocked frequencies of propagating elastic waves, in a periodic structure by designing the shape of an inclusion. This problem is modeled as a single unit cell using the time-harmonic elastodynamic wave equation with Floquet (periodic) boundary conditions. After discretization, an eigenvalue solver is used to compute the allowed frequencies of propagation for a certain wave vector. The geometry optimization method uses a tree structure to define geometry: internal tree nodes represent a priority-based overlap and leaf nodes contain a list of points whose convex hull represent a convex polygon. A genetic programming method is used to optimize this data structure. Several bandgap structures are designed using different materials, unit cell shapes, and total number of available materials. The results show that bandgaps exist for several different material systems though typically not just between the first and second bands. In addition to the inclusion shape, the size of the bandgap usually depends on the materials, with materials systems having large differences in wave speeds producing larger gaps.
Distribution: Approved for public release
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Last Update / Reviewed: September 1, 2011