## 5 Results and Discussion
\begin{table}
\begin{tabular}{l l l l} \hline \hline \(B\), \(\gamma\) = 4.56 & \begin{tabular}{l} **First Critical Speed** \\ **Amplitude Value** \\ \end{tabular} & \
\begin{tabular}{l} **Second Critical** \\ **Speed** \\ **Amplitude Value** \\ \end{tabular} &
\begin{tabular}{l} **Third Critical Speed** \\ **Amplitude Value** \\ \end{tabular} \\ \hline \(b_{m}=0\) & 0.110805396, \(\tau\) = 0.16 & 0.292896271, \(\tau\) = 0.69 & 1.917205238, \(\tau\) = 1.76 \\ \(b_{m}=0.5\) & 0.110797785, \(\tau\) = 0.16 & 0.292762234, \(\tau\) = 0.69 & 1.915895568, \(\tau\) = 1.76 \\ \(b_{m}=5\) & 0.110729214, \(\tau\) = 0.16 & 0.286890823, \(\tau\) = 0.69 & 1.710435466, \(\tau\) = 1.76 \\ \(b_{m}=25\) & 0.110422857, \(\tau\) = 0.16 & 0.205546804, \(\tau\) = 0.69 & 0.558152699, \(\tau\) = 1.76 \\ \(b_{m}=50\) & 0.110036396, \(\tau\) = 0.16 & 0.124228936, \(\tau\) = 0.69 & 0.231023687, \(\tau\) = 1.76 \\ \(b_{m}=100\) & 0.10925273, \(\tau\) = 0.16 & 0.066849372, \(\tau\) = 0.69 & 0.104944945, \(\tau\) = 1.76 \\ \(b_{m}=500\) & 0.102684806, \(\tau\) = 0.16 & – & – \\ \(b_{m}=5000\) & 0.08448214, \(\tau\) = 0.15 & – & – \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Critical Speeds. Figure 3: Amplitude–frequency characteristics of natural oscillations of the foundation for \(s=1\) and \(\gamma=13.8\). When the rotor cavity is filled with liquid by one third, i.e., at \(\gamma=2.6\), the system still has three critical frequencies (\(\tau=0.16\), \(\tau=0.64\) and \(\tau=2.14\), see Figures 6 and 7). In this case, the maximum values of the rotor amplitudes at the third critical frequency are 19.8-fold greater than the amplitudes in the similar case at \(\gamma=4.56\) (\(b_{m}=0\)), whereas the amplitudes \begin{table}
\begin{tabular}{l l l l} \hline \hline \(D\), \(\gamma=4.56\) & \begin{tabular}{l} **First Critical Speed** \\ **Amplitude Value** \\ \end{tabular} & \
\begin{tabular}{l} **Second Critical** \\ **Speed** \\ **Amplitude Value** \\ \end{tabular} &
\begin{tabular}{l} **Third Critical Speed** \\ **Amplitude Value** \\ \end{tabular} \\ \hline \(b_{m}=0\) & 0.07047227, \(\tau=0.16\) & 0.226388549, \(\tau=0.69\) & 1.704994351, \(\tau=1.76\) \\ \(b_{m}=0.5\) & 0.070468917, \(\tau=0.16\) & 0.226287308, \(\tau=0.69\) & 1.70381006, \(\tau=1.76\) \\ \(b_{m}=5\) & 0.07043893, \(\tau=0.16\) & 0.221699183, \(\tau=0.69\) & 1.520112352, \(\tau=1.76\) \\ \(b_{m}=25\) & 0.070309814, \(\tau=0.16\) & 0.157597686, \(\tau=0.69\) & 0.488944743, \(\tau=1.76\) \\ \(b_{m}=50\) & 0.070157935, \(\tau=0.16\) & 0.034896767, \(\tau=0.7\) & 0.194103909, \(\tau=1.76\) \\ \(b_{m}=100\) & 0.069885617, \(\tau=0.16\) & 0.045941501, \(\tau=0.69\) & 0.072065559, \(\tau=1.76\) \\ \(b_{m}=500\) & 0.069093807, \(\tau=0.16\) & 0.012824952, \(\tau=0.7\) & 0.010085603, \(\tau=1.77\) \\ \(b_{m}=5000\) & 0.089252733, \(\tau=0.16\) & – & – \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 4: Amplitude–frequency characteristics of natural oscillations of the rotor for \(\gamma=4.56\), \(s=1\). Figure 5: Amplitude–frequency characteristics of natural oscillations of the foundation for \(\gamma=4.56\), \(s=1\). of the second critical frequency are comparable with the previous case. An increase in the parameter that determines the influence of the magnetic field on a fluid particle from 0 to 0.5 leads to damping of the rotor and foundation amplitudes corresponding to the third critical frequency [28]. A significant decrease in the amplitudes of the second critical frequency occurs with an increase in \(b_{m}\) to 25. Further, as \(b_{m}\) increases to 500, the amplitudes of the second and third critical frequencies are almost completely suppressed. A change in the parameter that determines the influence of the magnetic field on a liquid particle has practically no effect on the amplitudes of the first critical frequency, except for large values of the magnetic field strength.