## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter Value**} & \multicolumn{4}{c}{**First Resonance**} & \multicolumn{4}{c}{**Second Resonance**} \\ \cline{2-7}  & **Frequency** & **Rotor’s** & **Foundation’s** & **Frequency** & **Rotor’s** & **Foundation’s** \\  & **-\(\omega_{f}\)** & **Amplitude-\(f_{1}\)** & **Amplitude-\(f_{2}\)** & **-\(\omega_{f}\)** & **Amplitude-\(f_{1}\)** & **Amplitude-\(f_{2}\)** \\ \hline \(\varepsilon=0.1\) & & & 9.8 & 5 & 1.15 & & \\ \hline \(\varepsilon=0.5\) & & & 8 & 3.95 & 1.2 & & \\ \hline \(\varepsilon=1\) & 0.051 & & 5.023 & 3.564 & 1.301 & 12.554 & 1.954 \\ \hline \(\varepsilon=5\) & & & 3.95 & 3.25 & 1.4 & & \\ \hline \(\varepsilon=10\In the case of an increase in the damping coefficients of the rotor and the foundation (Figures 7 and 8: cases \(\zeta_{1}\) = 5 and \(\zeta_{2}\) = 5, \(\zeta_{1}\) = 10 and \(\zeta_{2}\) = 10), the amplitudes for both the first and the second resonant regions decrease. For example, at \(\zeta_{1}\) = 5 and \(\zeta_{2}\) = 5, the foundation and rotor amplitudes at the first and second resonances decrease by a factor of 1.5. In the case of an increase in damping by one order of magnitude, i.e., \(\zeta_{1}\) = 10 and \(\zeta_{2}\) = 10, the amplitudes of the foundation and the rotor at the first and second resonances already decrease by a factor of 2.15. Shifts in the region of both the first resonant frequencies and the second ones are not observed in these cases. As the damping decreases  
Figure 5: The amplitude-frequency characteristic of the rotor at various degrees of non-linearity. Figure 6: The amplitude-frequency characteristic of the foundation at various degrees of non-linearity. With an increase in the mass of the rotor (Figures 9 and 10: cases \(\mu=10\) and \(\mu=5\)), an increase in the amplitudes of the rotor and foundation is observed in all areas of resonant frequencies. In the case of a fivefold increase in the mass of the rotor, i.e., at \(\mu=5\), the rotor amplitude increases by a factor of 1.4, and the foundation amplitude by a factor of 1.1. With a further increase in the mass ratio, the amplitudes also increase, for example, at \(\mu=10\), the difference in the amplitude ratios with the case of \(\mu=1\) already reaches 2.25 times. With an increase in the mass of the foundation (Figures 9 and 10: cases \(\mu=0.5\) and \(\mu=0.1\)), in all cases and in all areas of resonant frequencies, a decrease in the amplitude values is observed, since in these cases the foundation acts as an anti-weight and dampens the oscillations of the system as a whole. For example, the values of the amplitudes at \(\mu=0.5\) for the rotor decrease in magnitude by 1.06 times, and for the foundation by 1.27 times. With a further increase in the mass of the foundation, the decrease in the amplitudes is more intense and is already less than for the case \(\mu=1\) by 2 and 1.97 times. The values of frequencies and amplitudes for different values of the mass ratio parameter are presented in more detail in Table 5 and in Figures 9 and 10. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{3}{c}{**First Resonance**} & \multicolumn{3}{c}{**Second Resonance**} \\ \cline{2-7}  & **Frequency** & **Rotor’s** & **Complitude-\(f_{1}\)** & **Complitude-\(f_{2}\)** & **Frequency** & **Rotor’s** & **Foundation’s** & **Complitude-\(f_{1}\)** & **Complitude-\(f_{2}\)** \\ \hline \(\mu=0.1\) & & 2.5 & 2 & & 5.87 & 0.8 \\ \hline \(\mu=0.5\) & & 4.7 & 2.75 & & 8.5 & 1.01 \\ \hline \(\mu=1\) & 0.051 & 5.023 & 3.564 & 1.301 & 12.554 & 1.3 \\ \hline \(\mu=5\) & & 7 & 3.9 & & 15.25 & 1.8 \\ \hline \(\mu=10\) & & 11.25 & 4.25 & & 18.15 & 2.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Amplitudes and resonant frequencies for different mass ratios. Figure 8: The amplitude-frequency characteristic of the foundation at different values of damping coefficients.