###### Abstract
[6] dealt with the simulation of the transient run-up of rotors supported by fluid film bearings. The model they developed consists of a rotor represented by a flexible multibody system and bearings discretized with finite elements. The conducted research was aimed at the cognition of different behavior of two design variants of a turbocharger when the bearings were either fully submerged in the oil bath or worked in the air environment. [PERSON] et al. [7] performed a transient analysis of a speed-varying rotor, focusing on the influence of uncertain parameters. The effort was aimed at reducing errors in calculations. [PERSON] et al. [8] focused on the response analysis of an accelerating overhung rotor affected by random and uncertain values of a number of physical parameters. The developed approach provides guidance for the accurate transient dynamic analysis of engineering problems with hybrid uncertainties. The behavior of rotor systems is significantly affected by stiffness and damping of their supports, which can be utilized to control their vibration. Several design possibilities, based on mechanical, hydraulic, piezoelectrical, or electromagnetic principles, have been developed, researched, and tested. The mechanical way of changing the support stiffness described by [PERSON] et al. [9] consists in changing the length of the elastic spring. Another possibility regarding how to change the stiffness of the structure supports is represented by piezoelectric devices. For example, the stiffness of a lead-zirconate-titanate piezoceramic actuator with short-circuited electrodes on its faces is smaller by about 20-40% than in the case when the opposite faces of the actuator are not electrically connected. The controlled change in the stiffness of a rotor by a bearing movable in the axial direction is reported in [10]. A further possibility is the usage of smart memory metals [11]. [PERSON] and [PERSON] [12] reported on an active journal bearing, the stiffness of which is controlled by the change in the oil influx into the bearing gap. The effect of different geometries on the performance of hydrodynamic bearings was investigated by [PERSON] et al. [13]. The modeling of a controllable bearing with three flexible sleeves can be found in [14]. A wide class of active rotor support elements employs piezoelectric materials. [PERSON] presented a journal bearing [15; 16], the active part of which is a piezoelectric ring that, under application of the electric field, changes its radial dimension and influences the size of the bearing clearance. [PERSON] et al. [17] introduced a new reluctance electromagnetic damper intended for aero-engine applications. Utilization of smart liquids sensitive to a magnetic field used as lubricants of hydrodynamic bearings or squeeze film dampers has been a subject of theoretical and experimental research for many years [18; 19; 20; 21]. The set-up of new mathematical models of magnetorheological dampers and bearings developed by [PERSON] et al. [22; 23] is a contribution to the development in this area. The Bingham and bilinear (biviscous) materials were used to represent the lubricating oil. The influence of the delayed yielding of magnetorheological oils in damping elements on the vibration attenuation of rotors was investigated by [PERSON] and [PERSON] [24]. [PERSON] et al. [25] analyzed the possibility of using the magnetorheologicaloils as lubricating liquids of hydrodynamic bearings with the aim to control the rotor behavior. Their research shows that activation of magnetorheological lubricants leads to suppression of the rotor lateral vibration and changes the critical speeds. [PERSON] et al. [26] conducted a study on a floating ring bearing lubricated by magnetorheological fluid. The goal of the analysis was to determine the bearing stiffness and damping coefficients and testing the ability of the rotor vibration control by means of changing magnetic induction in the bearing gap. [PERSON] et al.