Beyond Common Simplifications: Strongly Nonlinear Transient Phenomena

Dynamics of transient strongly nonlinear phenomena develops rapidly, both at fundamental level and in view of multiple current and prospective applications. Intrinsic difficulty of the subject lies in the fact that many common notions and well-developed concepts of nonlinear dynamics, such as steady-state responses, bifurcations, nonlinear normal modes and many others, are not directly relevant, or at least hardly applicable in this sort of problems. Thus, the analysis and understanding of these phenomena require thinking beyond the aforementioned common simplifications. The paper offers a hands-on introduction to two topics within the broader subject of the transient strongly nonlinear phenomena. The first, more common and classical, is the dynamics of escape form classical potential well in conditions of external forcing. The other is an emerging topic of intermodal targeted energy transfer for purposes of enhanced blast and earthquake mitigation. For both topics, the paper presents simple introduction with basic developed examples. Brief descriptions of recent progress are accompanied by appropriate references.