## 4 Conclusions  
Through theoretical analysis, numerical analysis, and experimental verification, the following conclusions can be drawn:  
1. The influence of the support stiffness on the critical speed of the unbalanced single-side cantilevered rotor system shows that when the support stiffness is greater than \(1.5\times 10^{7}\) N/m, the critical speed does not change. Therefore, a novel type of integral squeeze film bearing damper is designed. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Working Condition** & \begin{tabular}{c} **1\(\times\) (\(\upmu\)m)** \\ **(\({}^{1}\) Exp)** \\ \end{tabular}  & \begin{tabular}{c} **1\(\times\) (\(\upmu\)m)** \\ **(\({}^{2}\) Th)** \\ \end{tabular}  & \begin{tabular}{c} **2\(\times\) (\(\upmu\)m)** \\ **(\({}^{1}\) Exp)** \\ \end{tabular}  & \ \begin{tabular}{c} **2\(\times\) (\(\upmu\)m)** \\ **(\({}^{1}\) Exp)** \\ \end{tabular}  & \begin{tabular}{c} **3\(\times\) (\(\upmu\)m)** \\ **(\({}^{2}\) Th)** \\ \end{tabular}  \\ \hline Working condition 1 & 891.39 & 856.83 & 43.47 & 38.43 & 13.27 & 12.13 \\ Working condition 2 & 862.73 & 821.32 & 36.19 & 31.07 & 12.32 & 10.01 \\ Working condition 3 & 702.51 & 688.32 & 25.33 & 23.93 & 9.16 & 7.71 \\ Working condition 4 & 591.27 & 568.86 & 17.14 & 14.13 & 6 The stiffness of the ISFBD is designed to be \(5\times 10^{6}\) N/m by numerical analysis, which ensures that the stiffness meets the design requirements and ensures the strength of the ISFBD structure. 2. Through numerical analysis, the influences of ISFBD installation position and quantity on system stability and energy distribution is verified. Studying the installation position shows that installing an integral squeeze film bearing damper near the cantilevered end can make the system more stable, and can share 20.49% of the energy at the support. A study of the quantity of dampers shows that installing two dampers makes the system more stable than installing one damper, while allowing 32.81% of the energy of the system to be shared. 3. Under the unbalanced excitation of 0.15 g\(\cdot\)m at the cantilevered end, it is verified that installing the ISFBD at the appropriate position can change the critical speed of the system and effectively avoid resonance. 4. At the same time, the quantity and position of integral squeeze film bearing dampers are investigated to reduce the vibration of the unbalanced single-side cantilevered rotor system. The numerical results are in good agreement with the experimental results. By analyzing the time and frequency domains at the given speed, it can be seen that installing the damper near the cantilevered end has a better vibration control effect, which can reach 20.41% in the time domain spectrum. The damping effects of 1 \(\times\), 2 \(\times\), and 3 \(\times\) frequencies in the frequency domain spectrum are 21.19%, 41.73%, and 30.97%, respectively. If two ISFBDs are installed, they can reach 34.59% in the time domain spectrum, and the damping effects on the 1 \(\times\), 2 \(\times\), and 3 \(\times\) frequencies in the frequency domain spectrum are 33.67%, 60.57%, and 50.26%, respectively. This can provide some guidance for practical engineering applications. Installing an integral squeeze film bearing damper close to the cantilevered end or changing the supports to integral squeeze film bearing dampers leads to better vibration control. Vibration control of the unbalanced single-side cantilevered rotor system using ISFBD needs further research, mainly in the following aspects:  
1. Some conditions were limited and simplified in the process of establishing physical models, and further analysis of the theory and exploration of practical applications is still needed. For example, during numerical simulations and experiments, the effects of vibration on the unbalanced single-side cantilevered rotor system when the system takes in or discharges fluid were not considered. 2.