## 3 Results and Discussions
### The Dynamic Responses of Rotor System Fan before and after Bird Strike
Looking at the plots from \(t=3\) s to \(t=3.5\) s, it can be seen that the amplitude of the rotor displacement is modulated after the onset of the shock, showing the multi periodic motion and the response amplitude gradually decreases under the effect of damping, and that the motion is eventually is smoothed out and goes back to the situation before the impact. As the research did not consider the deformation of fan blades and the fan blade-out events during bird strike, the operation of the rotor system goes back to normal after bird strike. From the axial orbit diagram in Figure 12f, it can be seen that, after the bird strike, the fan motion has deviated significantly from circular axial orbit curves in Figure 12e. It shows multiple chaotic intersecting curves with intense and irregular variations. The amplitude of motion also increases significantly compared to the stable operation before bird strike occurrence. However, there exists a clear stable region in the middle of the axial diagram (Figure 12h). Meanwhile, it can be seen from the phase diagram (Figure 12h) that there are multiple limit rings of motion during this period, that the situation is chaotic, and that several overlapping situations occur. At the end of bird strike phenomenon, a stable limit ring appears in the middle of the phase diagram (Figure 12h) and Poincare section map (Figure 12j). There are several points in the Poincare section map due to the bird strike, which indicate multiple cycles of the motion which gradually converge to a fixed position. From above-mentioned analysis, it can be concluded that a bird strike on an aero-engine operating at 3772 r/min causes a strong transient impact on the rotor system, and that the rotor motion will be greatly disturbed, affecting the normal operation of the rotor. However, due to the instantaneity of the impact, the rotor system gradually regains its stability due to damping effect after the shock. It can be seen in Figure 12l that after the rotor is impacted by the bird, the rotor rotation frequency still exists, even though it has a slight increase in amplitude compared to stable operation. A sharp peak is produced at frequency of 43.2 Hz. This frequency is independent of the fundamental frequency, which is due to the bird strike exciting the first mode of the rotor. The time-frequency graph of the dynamic response before and after bird strike in the x direction is demonstrated in Figure 12m,n. During \(t=2\)-\(2.5\) s, the frequency band in the graph is concentrated on the position of the rotational frequency, as the bird strike had not occurred at this time. After the bird strike occurring at 3 s, a clear abrupt change in frequency emerges. In addition to the fundamental frequency of 62.9 Hz, a frequency of 43.2 Hz has appeared, which is approximately equal to the first-order mode. The first-order response of the rotor system (43.2 Hz) was excited by the transient shock caused by the bird strike. In summary, the rotor motion becomes extremely unstable after a bird strike; therefore, corresponding measures must be taken, otherwise it will cause great harm to the normal operation of the aircraft engine.