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Article

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

Vorotnikov K., Kovaleva Margarita, Starosvetsky Y.

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 subject to initial or harmonic loading 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, uni-directional 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. Present review will comprise the 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 the two-dimensional ones.