The aim of this work has been to obtain mathematical expressions for the effective acoustic parameters of heterogeneous systems in the homogenization limit, what has allowed the design of new refractive devices working in a wide wavelength range.
Mathematically this problem has been treated by means of the multiple scattering theory, because the geometries of the problem are mainly circular and such theory is the best one in this case.
To obtain the effective parameters two homogenization methods have been developed, which has been shown to be complementary. The first is based in elastic wave propagation through periodic media while the second is based in the acoustic scattering properties of finite clusters of cylinders.
The main applications of the developed theory are, due to its interest and novelty in the field of acoustics, the gradient index lens and the acoustic cloaking devices. These lenses are materials where the propagation speed of sound change as a function of the spacial coordinates, allowing then the control of the sound trajectory. In this work has been proposed one of these lenses with the peculiarity of being fully transparent, and then, all the incident energy is located at the focus of the lens.
Acoustic cloaking devices can hide inside them an object such that it be undetectable for sound. The complexity of these consists in that they have to be made of materials with an anisotropic mass density. This work has shown how to design these devices by means of cylinder structures made of two types of isotropic materials.