Emergence of non-stationary regimes in one- and two-dimensional models with internal rotators

In the present paper, we give a selective review of some very recent works concerning the non-stationary regimes emerging in various one- and two-dimensional models incorporating internal rotators. In one-dimensional models, these regimes are characterized by the intense energy transfer from the outer element, subjected to initial or harmonic excitation, to the internal rotator. As for the two-dimensional models (incorporating internal rotators), we will mainly focus on the two special dynamical states, namely a state of the near-complete energy transfer from longitudinal to lateral vibrations of the outer element as well as the state of a permanent, unidirectional energy locking with mild, spatial energy exchanges. In this review, we will discuss the recent theoretical and experimental advancements in the study of essentially nonlinear mechanisms governing the formation and bifurcations of the regimes of intense energy transfer. The present review is composed of two parts. The first part will be mainly devoted to the emergence of resonant energy transfer states in one-dimensional models incorporating internal rotators, while the second part will be mainly concerned with the manifestation of various energy transfer states in two-dimensional ones. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.