Nonlinear Periodic Phononic Structures and Granular Crystals

Abstract

This chapter describes the dynamic behavior of nonlinear periodic phononic structures, along with how such structures can be utilized to affect the propagation of mechanical waves. Granular crystals are one type of nonlinear periodic phononic structure and are the focus of this chapter. The chapter begins with a brief history of nonlinear lattices and an introduction to granular crystals. This is followed by a summary of past and recent work on one-dimensional (1D) and two-dimensional (2D) granular crystals, which is categorized according to the crystals’ periodicity and dynamical regime. The chapter is concluded with a commentary by the authors, which discusses several possible future directions relating to granular crystals and other nonlinear periodic phononic structures. Throughout this chapter, a richness of nonlinear dynamic effects that occur in granular crystals is revealed, including a plethora of phenomena with no linear analog such as solitary waves, discrete breathers, tunable frequency band gaps, bifurcations, and chaos. Furthermore, in addition to the description of fundamental nonlinear phenomena, the authors describe how such phenomena can enable novel engineering devices and be applied to other nonlinear periodic systems.