## 4 Conclusions  
The \"0-2-1\" rotor system model was modeled mathematically and combined with the bird strike force obtained from bird strike simulation in LS-DYNA; the responses of the rotor system under bird strike and at different rotational speeds were studied. The conclusions can be summarized as follows:  
(1) In the process of the bird strike, due to the blade geometry, the impact force in the y direction is much smaller than that in the x direction at 3772 r/min, with a difference of about 99.5 kN. The same holds true for other operational speeds. As the bird body in the bird strike process is cut into multiple parts, there are several peaks in the bird impact force diagrams.  
(2) At the climbing state, the dimensionless displacement in the x direction was 0.88 before bird strike, and it reached 14 after bird strike, which shows an increase of about 16 times. The motion type also changed from a single periodic type to irregular quasi-periodic type. The displacement of the rotor system also increased significantly, and the closer to the fan hub, the more obvious the increase in amplitude. Therefore, bird strike has a serious impact on the rotor operation.  
(3) At different rotational speeds, the response of the rotor after bird strike is similar. The difference caused by speed is only reflected in the amplitude, as it leads to different impact forces. At 836 r/min, the displacement in the x direction increases from 0.05 before bird strike to 0.53 after bird strike, which is an increase of about 10 times. The increase is 16 times at 3772 r/min. The maximum value is much larger than that at a low rotational speed. Therefore, the higher the rotational speed, the greater the damage caused by a bird strike is.  
(4) The frequency spectrums at all four speeds show a peak at 43 Hz. Combined with the natural frequency of the rotor, bird strike excites the first-order vibration of the rotor.  
This paper does not simply analyze the process of bird impact on the fan blade, but combines the bird impact process with the study of rotor system dynamics to obtain the rotor system dynamics response when the rotor system is struck by a bird, which is of guiding significance for the dynamics analysis of aero engines under bird strike, and the conclusions obtained also provide ideas for the safety design of aero engines; for example, bearing force can be used to guide the design of bearing structure, which is very effective in suppressing the vibrations caused by bird strikes.  
Conceptualization, B.W. and J.Z.; methodology, B.W. and J.L.; software, B.W. and G.Z.; validation, B.W., J.Z. and L.Z.; resources, R.H. and L.Z.; data curation, J.Z.; writing--original draft preparation, B.W.; writing--review and editing, R.H.; supervision, L.Z.; project administration, J.Z.; and funding acquisition, G.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Joint Funds of National Science Foundation of China and Civil Aviation Administration Foundation of China, grant number U1833108.  
The data presented in this paper are available on request from the corresponding author.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.