Nonsmooth processes as asymptotic limits

Abstract

In this chapter, we consider different physical models generating both smooth and nonsmooth temporal mode shapes as appropriate conditions occur. The objective is to bring attention to the fact that nonsmooth processes may naturally occur as high-energy asymptotics in different oscillatory models with no intentionally introduced stiff constraints or external impacts. In other words, nonsmooth temporal mode shapes may be as natural as sine waves generated by oscillators under low-energy conditions. Essentially nonlinear phenomena, such as nonlinear beats and energy localization are also considered. In particular, it is shown that energy exchange between two oscillators may possess hidden nonsmooth behaviors.