## 5 Results and Discussion  
To evaluate the dependence of the damping and shift in frequencies of natural oscillations on the magnetic field, the operation of the rotor system with different values of parameters \(b_{m}\) and \(\gamma\) at the maximum amplitudes of the rotor system, which are observed at the main resonance, i.e., at \(s=1\), was considered (see Figures 2-11). In the general case, three critical frequencies are observed in the system (see Figures 2 and 3). This means that due to the presence of liquid even in a small amount in the rotor cavity, two additional critical frequencies are superimposed with amplitudes, the values of which increase until the cavity is filled by one third [20]. A further increase in the amount of liquid in the cavity leads to the complete suppression of the second critical frequency, thus, at \(\gamma=1\) (complete filling of the cavity with liquid), two critical frequencies will be observed in the system. An increase in the value of the parameter that characterizes the effect of a magnetic field on a liquid particle, in general, positively affects the dynamics of the system. When varying the \(b_{m}\) parameter, a significant influence is observed for the amplitudes at the third critical frequency [21]. With an increase in \(b_{m}\), the amplitudes of the second critical frequency are damped more weakly, and the amplitudes of the first critical frequency practically do not change, as they are also present in the absence of liquid in the rotor cavity. It should be noted that at a sufficiently high magnetic field strength, i.e., at \(b_{m}=5000\), the oscillations of the system are practically similar to the case of an empty rotor, as the liquid in this case, as if \"solidifies\" and behaves like a solid body [22]. No shift in critical frequencies is observed in all cases, except for \(b_{m}=5000\). For clarity and convenience of application of the results in engineering practice, the authors plotted the dependencies of critical amplitudes for different values of the parameters \(b_{m}\) and \(\gamma\) (see Figures 2 and 3). With a small amount of liquid in the rotor cavity, for example, at \(\gamma=13.8\) (\(r_{0}=0.93R\)), three critical frequencies are observed at \(\tau=0.16\), \(\tau=0.78\), and \(\tau=1.36\), and three zones of self-oscillations, the maximum amplitudes of the rotor and foundation are observed at the third critical speed in cases \(b_{m}=0.100\). Due to the small amount of liquid, the second critical frequency has smaller amplitudes compared to the first. With an increase in the \(b_{m}\) parameter to \(500\), a slight shift in the second and third critical frequencies is observed towards an increase in the angular velocities of the rotor rotation [23; 24]. In the case of a sufficiently high magnetic field strength, the second critical frequency shifts in the direction of increasing dimensionless frequency up to \(\tau=1\), whereas the third critical frequency of the rotor and foundation is completely damped. The numerical values of the amplitudes for this case are presented in Table 1. Dashes in the table indicate the absence of critical frequencies or the complete damping of the natural oscillation amplitudes in this interval (25).