Granular materials are collections of macroscopic grains that interact via dissipative and nonlinear forces. These materials display a complex behavior which remains a challenging problem. The better understanding of this behavior is of great practical importance in pharmaceutical and food industries as well as in natural processes such as land sliding and avalanches. In addition, granular media are offering new insights into problems in condensed-matter physics, geophysics and materials science.The last years, several insights have been obtained by applying statistical mechanics to study granular media. Nowadays, it is clear that nonlinear effects play a crucial role. This proposal, which resides at the interface of nonlinear dynamics, acoustics, and condensed matter physics, seeks to extend the state-of-the-art techniques, introducing tools and concepts from nonlinear and chaotic dynamics. The main objectives are: (1) a better understanding of the physics of driven granular media, (2) the design of granular-based acoustic devices for the control of acoustic propagation.We aspire to achieve the research objectives by employing a synergistic approach that combines theoretical techniques, computational methods, and experiments. In particular, we will study highly nonlinear processes, and their role in chaotic energy transport along a monodisperse chain. We will also examine the interplay of nonlinearity and disorder in polydisperse chains, a topic that has spurred great interest in recent years. In addition, we will study the role of frictional/hysteretic nonlinearities starting with 1D alignment which include the possibility of shear motion. Then, we will revisit the problem of energy transport in driven 2D granular solids.In parallel to the above activities, nonlinear processes will be studied in complex granular-based structures. These include locally resonant granular media and structures composed of linear elastic media and granular solids.