We are interested in vibrating systems, with applications of nonlinear behavior. The subject of this work deals with a special class of hybrid systems, that is, a vibrating system that combines electrical and mechanical drivelines. This paper is devoted to present a review concerning some properties of recent research progresses of non-ideal rotary support structures (RNIS) in the recent years restricted, however, to English publications only. In summary, we presented mathematical modelling of problems related to (RNIS), which render descriptions that are close to real situations found in practice. We were interested to what happens to the motor (or electro-mechanical shaker), input, output, as the response of the rotary system (RNIS) support structure changes, that is, we considered nonlinear resonances, including periodic, quasiperiodic, and chaotic characteristics in the steady state motions, and energy transfer between the energy sources and the support structures. Their possible control approaches are also considered to pass to resonance. This work is in honor for MI SANU.