Optimization of the Acoustic Systems

Introduction

A genetic algorithm is a global search method based on a simile of the natural evolution. Genetic Algorithms have demonstrated good performance for difficult problems where the function to minimize is complicated. In this work we applied this optimization method to improve the acoustical properties of the Sonic Crystal (Martínez-Sala et Al.,1995) (Kushwaha et al., 1994), a kind of structures used in acoustics.

In the last few years the propagation of the acoustic waves in heterogeneous materials whose acoustic properties vary periodically in space have attracted considerable interest. The so-called Sonic Crystals are the typical example of this kind of materials in the range of the acoustic frequencies. These systems are defined as periodic structures with strong modulation of the elastic constants between the scatterers and the surrounding material.

Recently, the strategy to enhance Sonic Crystals properties has been based on the use of scatterers with acoustical properties added. The use of local resonators (Liu et al., 2000) or Helmholtz resonators (Hu et al., 2005) as scatterers have produced very good results Some authors also have built new structures with scatterers made up of porous material improving the attenuation capability of the Sonic Crystals (Umnova et al., 2006). However, the use of Sonic Crystals as outdoor acoustic barriers requires scatterers made up of robust and long-lasting materials. This is the reason why it seems interesting to analyze the possibility of optimizing the attenuation capability of Sonic Crystals made with rigid scatterers like wood, PVC or aluminium. The creation of vacancies in a Sonic Crystals improves the attenuation capability of the Sonic Crystals (Caballero et al., 2001). However, it does not exist any generic rule about the creation of vacancies in a Sonic Crystals. In fact, similar structures can produce very different acoustic fields behind of them.

Because of the complexity of mathematical functions involved in Sonic Crystals calculus, Genetic Algortihm turns up as a tool specially indicated for this kind of problems (Hakanson et al., 2004) (Romero-García et al., 2006). This procedure can work together with the Multiple Scattering theory which is a self-consistent method for calculating the acoustic pressure including all orders of scattering (Chen & Ye, 2001). Given a starting Sonic Crystals, the Genetic Algorithm generates quasi ordered structures offspring by means of the creation of vacancies that are classified in terms of a cost function based on the pressure values at a specific point. The sound scattered pressure by every structure analyzed by Genetic Algorithm is performed by a two-dimensional (2D) Multiple Scattering theory. In the present work, it is shown an improvement of the Genetic Algorithm based on Parallel implementation and as a consequence, new and better results are obtained to design Quasi Ordered Structures made with rigid cylinders that attenuate sound in a predetermined band of frequencies.