## 3 Results
Figure 4: The amplitude-frequency characteristic of the foundation. is not observed in the linear case and is a multiple of the main one, it was found that it is an ultraharmonic resonance. It should be noted that in all the above cases, the main disadvantage of using the numerical method for the nonlinear case is the impossibility of determining the amplitudes of the rotor and the foundation for the amplitudes lying behind the break point. In the case of using the [PERSON] method, large deviations are observed both for the amplitudes and for the resonant frequencies. [PERSON]'s method of elliptic functions is free from these shortcomings due to its generality. To optimize the workflow using the method of elliptic functions, a parametric analysis was carried out by constructing the amplitude-frequency characteristics of the rotor and foundation for different values of the nonlinearity parameter \(\varepsilon\) (Figures 5 and 6), for different values of the damping coefficients \(\zeta_{1}\) and \(\zeta_{2}\) (Figures 7 and 8), for different values of the linear stiffness parameter \(\lambda\) (Figures 9 and 10), and for different values of the mass ratio of the foundation and the rotor \(\mu\) (Figures 11 and 12). All variable parameters are reduced to dimensionless form according to (9). An increase in the nonlinearity parameter up to one order of magnitude inclusive (Figures 5 and 6: cases \(\varepsilon=5\) and \(\varepsilon=10\)) leads to a decrease in the amplitudes of the rotor and foundation in the region of the first resonance. For example, for \(\varepsilon=5\), the rotor amplitude decreases by a factor of 1.26, while the foundation amplitude decreases by a factor of 1.08. Further, with an increase in the nonlinearity parameter, i.e., for \(\varepsilon=10\), the decrease in amplitudes is also more intense. For the rotor, in this case, the amplitude relative to \(\varepsilon=1\) already decreases by a factor of 2.27, and for the foundation, by a factor of 1.4. With a decrease in the nonlinearity parameter within one order of magnitude, the opposite picture is observed (Figures 5 and 6: cases \(\varepsilon=0.1\) and \(\varepsilon=0.5\)). For example, for \(\varepsilon=0.5\), the rotor amplitude increases by 1.5 times, and the foundation amplitude by 1.13 times. In the case of a decrease in the nonlinearity parameter by one order of magnitude, i.e., when \(\varepsilon=0.1\), the increase in amplitudes is more intense and exceeds the initial values by a factor of 1.96 for the rotor and by a factor of 1.43 for the foundation. No shifts in the region of the first resonant frequencies are observed in these cases. The absence of a shift along the frequency axis of the first resonance is due to the linear nature of the oscillations in this region. In addition, as shown earlier, these resonant amplitudes arise solely due to mobility and oscillations of the foundation. In the region of nonlinear resonant frequencies, the magnitudes of the amplitudes do not depend on the variation of the nonlinearity parameter. With an increase in nonlinearity, the slope of the amplitude-frequency characteristic curve increases, and the amplitude breakdown point shifts in the direction of higher frequencies. For example, for \(\varepsilon=5\), the drop in amplitudes shifts to \(\omega_{f}=1.4\), whereas for \(\varepsilon=10\), a drop is already observed at \(\omega_{f}=1.43\). As the nonlinearity decreases, the slope of the curve correspondingly decreases, degenerating into a linear case. The frequency and amplitude values are given in more detail in Table 3 and in Figures 5 and 6. Variation of the nonlinearity parameter only affects the slope at the second resonance and the amplitude values, since the non-linearity is known to limit the magnitude of the amplitudes.