# Continuous Rotor Dynamics of Multi-Disc and Multi-Span
## 3 Numerical Simulations and Discussion
### Calculated Unbalance Response  
#### 3.3.1 Results  
Based on CRDAM, FEM and Ricatti, three curves, which represent the relation between unbalance responses and rotating frequencies, are obtained in Figure 15. They are calculated at #2 point of the computational example g3.3. According to Figure 15, it is found that the three obtained curves have the same trend. According to Figure 15a,b, the three curves, which are obtained from 0 to 50 Hz and 50 to 150 Hz, are well coincident. It is because that the first and second order critical frequencies are equal. However, from 150 to 400 Hz, the three curves are not well coincident. The unbalance response curves obtained by CRDAM and FEM coincide better than the curve obtained by Ricatti according to Figure 15c. According to Figure 15d,e, the curves obtained by CRDAM and FEM still coincide better from 300 Hz to 600 Hz than the curve obtained by Ricatti. The reason is that the values of the critical frequencies calculated by CRDAM and FEM coincide better than the value calculated by Ricatti. According to Figure 15f, the three curves from 600 to 1000 Hz are not well coincident near the seventh order critical frequency due to the difference of the seventh order critical frequency. However, the three curves are well coincident when the calculating frequencies are far from the seventh critical frequency. Figure 14: Relative error of calculated critical frequency of CDRAM to FEM and Ricatti to FEM when the rotor is supported by oil journal bearings. Moreover, similar phenomena can be found in simulations of the computational examples g1.1, g2.2, g1.2, g1.3, h1.1, h2.2, h3.3, h1.2, h1.3 g5.5, g1.4, g1.5, h4.4, h5.5, h1.4 and h1.5 whose results are shown in Figures A1-A16 in Appendix C.  
Figure 16 shown the three curves of relation between unbalance responses and rotating frequencies is obtained using the computational example g4.4. The three obtained curves have the same trend. However, according to Figure 16a, although the first order frequency values are almost equal, the three unbalance response curves are not well coincident near the first order critical frequency. The peak value of FEM amplitude curve is biggest. However, the three curves coincide well when the calculating frequencies are far away from the first order critical frequency. Figure 15: Calculated unbalance response of point #2 of g3.3: (**a**) 0–50 Hz; (**b**) 50–150 Hz; (**c**) 150–300 Hz; (**d**) 300–500 Hz; (**e**) 500–600 Hz; (**f**) 600–1000 Hz. According to Figure 16b, the three curves from 200 to 270 Hz are well coincident except near the second and third critical frequency. Since the second and third order critical frequency values calculated by CRDAM and FEM are equal, the two curves obtained by CRDAM and FEM coincide better than the curve obtained by Ricatti at the two critical frequencies. At the second order frequency, the peak value of FEM amplitude curve is the biggest. At the third order frequency, the peak value of Ricatti amplitude curve is the biggest. Figure 16: Calculated unbalance response of point #2 of g4.4: (**a**) 0–200 Hz; (**b**) 200–270 Hz; (**c**) 270–500 Hz; (**d**) 500–800 Hz; (**e**) 800–1000 Hz. According to Figure 16c, the three curves from 270 to 500 Hz are still well coincident except near the fourth and fifth order critical frequency. The two curves obtained by CRDAM and FEM coincide better than the curve obtained by Ricatti at the two critical frequencies. According to Figure 16d, the curve obtained by CRDAM is well coincident with the curve obtained by FEM when the frequency is smaller than the seventh order critical frequency. It is also coincident with the curve obtained by [PERSON] when the frequency is far away from the sixth and seventh order critical frequency. While from the seventh order critical frequency to 800 Hz, the curve obtained by CRDAM does not coincide with the two curves obtained by FEM and Ricatti at all. However, according to Figure 16e, the curve obtained by CRDAM is obviously not coincident with the two curves obtained by FEM and Ricatti.