Average Wave Propagation and Scattering in Random Particulate Media: a broad frequency range

This thesis presents theoretical results in the study of ensemble averaging of acoustic waves in random particulate media, which consists of a collection of randomly placed particles in a homogeneous background medium. The main advance in theory is the generalisation of a closure assumption known as the Quasi-Crystalline Approximation (QCA), which enables accounting for multiple scattering of waves between particles and walls. We perform numerical simulations of average reflection and transmission coefficients for layers of particulate media, which reproduce recent experimental findings, such as Fabry-Pérot resonances. These numerical simulations contribute to the modelling of non-invasive and non-intrusive ultrasound characterisation setups for determining statistical particle properties. On another front, we deduce simple formulae for frequency dependent effective-properties for a mixture of randomly placed sub-wavelength resonators. We explain how to use these formulae to design broadband multiple tunable band gaps, leading to novel acoustic disordered metamaterials. The effective-properties are validated against high-fidelity Monte Carlo simulations of wave transmission for moderately long wavelengths compared to the diameter of each resonator.