## 5 Conclusions  
This study presents a new optimization design method for the flexible RSS base, aiming to prevent the occurrence of severe vibration instability in the flexible RSS base-rotor system during high-speed operation. By combining experimental modal analysis \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Mode Order**} & \
\begin{tabular}{c} **Numerical Natural** \\ **Frequency/Hz** \\ \end{tabular} &
\begin{tabular}{c} **Measured Natural** \\ **Frequency/Hz** \\ \end{tabular} & \multirow{2}{*}{**Percentage Error/\%**} \\ \hline
1 & 30.34 & 32.07 & 5.71 \\
2 & 125.33 & 115.82 & \(-\)7.59 \\
3 & 135.75 & 135.06 & \(-\)0.51 \\
4 & 145.89 & 153.31 & 5.09 \\
5 & 272.17 & 272.08 & \(-\)0.03 \\
6 & 328.08 & 315.08 & \(-\)3.96 \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of simulated and experimental modes at a plate width of 7 mm. with theoretical modal analysis and finite element modeling, the first natural frequency of the RSS base was accurately determined. Building on this, the support plate was optimized using the equivalent static load model, changing the overall dynamic characteristics of the RSS base and preventing resonance from occurring. Dynamic response analysis was subsequently performed to determine the response at different rotational speeds within the set sweep frequency range. The main conclusions of this study are as follows:  
1. After performing a static analysis of the RSS base, it was found that there is a certain level of stress concentration at the tangential support plate. This suggests that the tangential support plate is a vital core component of the RSS base, and its structure and strength are essential for the overall integrity of the RSS base;
2. Through the use of the equivalent static load model for the optimization design of the tangential support plate, the overall first natural frequency of the RSS base was reduced, transitioning the base's dynamic characteristics from rigidity to flexibility. This also enabled the flexible RSS base to avoid resonance frequencies, validating the effectiveness of the equivalent static load model and providing a solid direction for optimizing the RSS base;
3. Compared to conventional methods, this study constructed a small-scale flexible RSS base test bench based on the simplified dynamic model of the entire system, which made the experimental process more convenient and efficient. This study has made a breakthrough in RSS base analysis, moving from theoretical to experimental levels, thus greatly reducing the research difficulty for RSS bases and offering a simple and effective implementation approach and theoretical basis for future research. The implementation of the proposed design in actual gas turbines will provide direction for practical manufacturing design needs, significantly reducing time and economic costs. This makes it much easier to avoid resonance frequencies for the gas turbine. Naturally, this also introduces new challenges, such as how to manage the connection between the modified tangential support plate and the overall components and how to ensure the strength of the support plate meets the requirements after modifications. These issues will be explored and refined in future research. Y.T. : Conceptualization, data curation, methodology, validation, supervision, writing--original draft preparation, writing--review and editing, project administration, investigation. G.T. : Conceptualization, resources, methodology, writing--review and editing, project administration, supervision, funding acquisition. H.H. : validation, project administration, investigation. M.G. : Conceptualization, methodology, writing--review and editing, supervision, methodology. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China Regional Fund Project, grant number 12162031, and the General Program of National Natural Science Foundation of China, grant number 11772289. Not applicable.