Nonlinear Phononic Periodic Structures and Granular Crystals.

摘要

In this chapter we describe the dynamic response of nonlinear phononic structures, focusing on granular crystals as the most prominent example. The chapter begins with a brief history of nonlinear lattices and with an introduction to granular crystals. It describes past and recent work on one- dimensional (1D) and two-dimensional (2D) granular crystals, categorized according to the crystals' periodicity and dynamical regime. It concludes with an overview of other nonlinear phononic systems and with a forelook into the future. Our purpose is to reveal the richness of the nonlinear dynamic effects including plethora of phenomena with no linear analogue such as solitary waves, discrete breathers, tunable frequency band gaps, bifurcations, and chaos. The extension of this study into other phononic structures could allow the observation of new physical phenomena at different scales, and lead to the design of novel engineering devices.