Shape-optimal design of graded index sonic crystal formations using natural cubic splines

Noise reduction through upward refraction can be achieved by artificial means, using a graded index sonic crystal. In addition to upward refraction, it will be shown that these periodically spaced cylinder formations can simultaneously benefit from band-gap phenomena. The aim of this paper is to present a method to optimise the broadband noise reducing performance of graded index sonic crystals, in a frequency range from well below to well above the lowest band-gap frequency. A design technique based on the creation of complex cylinder formations has been explored, in which the effective propagation speed is spatially varied using natural cubic splines. Sets of complex barrier shapes are compactly described by re-locating a number of control points in a two-dimensional cartesian plane and connecting the control points by (curved) line segments. In addition to the cluster shape, a complex graded index sonic crystal structure was formed by varying the lattice constant and the cylinder radius, where the cylinder radius was varied as a function of height. All these parameters were optimised with a multi-objective genetic algorithm, for structures based on horizontally oriented acoustically hard cylinders, located above a perfectly reflecting ground plane. A four-lane outdoor situation, with a traffic scenario consisting of 95% light and 5% heavy duty vehicles driving at 70 km/h has been studied in a two-dimensional domain. For such a configuration we obtained a spatially averaged mean reduction of 4.2–5.3 dBA, with structures covering an effective cross-sectional area of 1 m². It was found that the insertion loss among the studied traffic lanes was reasonably constant. In addition, it was found that the low-frequency performance of the studied structures is enhanced by incrementing the barrier-height while increasing the number of scatterers as a function of height.