## 3 Results and Discussions
### The Dynamic Responses of Rotor System Fan before and after Bird Strike  
The dynamic responses of the rotor system fan before and after bird strike are demonstrated in Figure 12. Figure 12a depicts the variations of the rotor displacement in the x direction vs. time in the steady-state operational condition when the bird strike has not yet occurred (\(t=2\)-\(2.5\) s). The periodic fluctuations of displacement in the x direction come from the interaction of eccentric force, stiffness and damping of the system. The system runs smoothly during this duration and the maximum dimensionless displacements \begin{table}
\begin{tabular}{c c c c} \hline
**Mass (kg)** & **Stiffness (N/m)** & **Damping (N-s/m)** & **Other Parameters** \\ \hline \(M_{R1}=294.75\) & \(K_{r}=3\times 10^{7}\) & \(C_{R}=2050\) & \(e_{R1}=5\times 10^{-5}\) m \\ \(M_{R2}=101.2\) & \(K_{b}=6\times 10^{7}\) & \(C_{B}=4200\) & \(e_{R2}=5\times 10^{-5}\) m \\ \(M_{\text{B1}}=25.2\) & & & \(\mu_{B}=1.1\times 10^{-4}\) m \\ \(M_{\text{B2}}=25.2\) & & & \(g=9.8\) m/s\({}^{2}\) \\ \(M_{\text{B3}}=25.2\) & & & \\ \hline \end{tabular}
\end{table} 
Table 2: The geometrical and material parameters of rotor system. remains constant at 0.8. Similarly, in Figure 12c, the same periodic motion can be observed, but in the y direction. With an initial displacement in the y direction due to the gravitational force, the amplitude range is \(-1.68\) to \(-2.98\). The system operated smoothly before the bird strike occurs. Figure 12e shows the axial rotation of the system in the steady-state operation, with the axis of the fan moving in the range of approximately \(-0.8\) to \(0.8\) in the x direction and \(-3\) to \(-1.8\) in the y direction. The axial rotation remains constant as a closed and relatively regular circle. Figure 12: Cont. Figure 12g shows the phase diagram of the rotor operation, where the trajectory line is demonstrated as a closed limit ring, indicating that the system has a single periodic motion. There is also only one isolated point in the Poincare section map in Figure 12i. Both diagrams in Figure 12g,i indicate that the rotor system undergoes a stable single periodic motion before bird strike. It can be seen from Figure 12k that there is no other frequency component, except the fundamental frequency in the spectrum graph, which confirms the correctness of the previous graph. It would be intuitive to investigate the effect of the bird strike on the noted graphs. Figure 12b,d depict the horizontal and vertical time history of the fan displacement after the occurrence of bird strike at \(t=3\) s. In the x direction, due to the influence  
Figure 12: The dynamic response of rotor system fan before and after bird strike at 3772 r/min: (**a**) time history of displacement before bird strike in the X direction, (**b**) time history of displacement after bird strike in the X direction, (**c**) time history of displacement before bird strike in the Y direction, (**d**) time history of displacement after bird strike in the Y direction, (**e**) axis orbit before bird strike, (**f**) axis orbit after bird strike, (**g**) phase diagram before bird strike, (**h**) phase diagram after bird strike, (**i**) the Poincaré section before bird strike, (**j**) the Poincaré section after bird strike, (**k**) frequency spectrum before bird strike, (**l**) frequency spectrum after bird strike, (**m**) time-frequency graph before bird strike, and (**n**) time–frequency graph after bird strike. of the applied bird impact excitation, the amplitude of the rotor displacement changes dramatically after \(t=3\) s, with a maximum dimensionless amplitude close to 15 in the x direction. In the y direction, the maximum displacement amplitude increases for around 3.7 times compared to the initial position, which is due to the larger bird impact force in the x direction. The difference between the x direction and y direction displacements before and after the bird strike demonstrates that the magnitude of the bird impact force has a direct effect on the displacement of the fan rotor.