Optimization of phononic filters via genetic algorithms

Abstract

A phononic crystal is commonly characterized by its dispersive frequency spectrum. With appropriate spatial distribution of the constituent material phases, spectral stop bands could be generated. Moreover, it is possible to control the number, the width, and the location of these bands within a frequency range of interest. This study aims at exploring the relationship between unit cell configuration and frequency spectrum characteristics. Focusing on 1D layered phononic crystals, and longitudinal wave propagation in the direction normal to the layering, the unit cell features of interest are the number of layers and the material phase and relative thickness of each layer. An evolutionary search for binary- and ternary-phase cell designs exhibiting a series of stop bands at predetermined frequencies is conducted. A specially formulated representation and set of genetic operators that break the symmetries in the problem are developed for this purpose. An array of optimal designs for a range of ratios in Young's modulus and density are obtained and the corresponding objective values (the degrees to which the resulting bands match the predetermined targets) are examined as a function of these ratios. It is shown that a rather complex filtering objective could be met with a high degree of success. Structures composed of the designed phononic crystals are excellent candidates for use in a wide range of applications including sound and vibration filtering. © 2007 IOP Publishing Ltd.