## 6 Conclusions  
In this paper, modal discretization and spatial discretization methods were presented and compared in the study of a flexible structure with distributed gyroscopes. Using the gyroscopic beam example, it was found that the modal discretization was more efficient when dealing with lower order vibration modes and the spatial discretization costs more computation time. The modal discretization method requires explicit mode functions of the base structure, which is not applicable to irregular components. The spatial discretization method allows manipulations of flexible structures of any shape, although the computation cost is higher. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **Order** & **1 BW** & **1 FW** & **2 BW** & **2 FW** & **3 BW** & **3 FW** & **4 BW** & **4 FW** \\ \hline \multirow{3}{*}{100} & Modal & 0.0374 & 0.146 & 0.322 & 0.341 & 0.549 & 0.817 & 1.100 & 1.201 \\  & Spatial & 0.0370 & 0.144 & 0.316 & 0.344 & 0.538 & 0.797 & 1.070 & 1.194 \\  & Deviation (\%) & 1.27 & 1.51 & 1.77 & \(-\)0.82 & 2.15 & 2.41 & 2.70 & 0.58 \\ \hline \multirow{3}{*}{200} & Modal & 0.0202 & 0.0782 & 0.173 & 0.291 & 0.431 & 0.526 & 0.573 & 0.710 \\  & Spatial & 0.0199 & 0.0768 & 0.169 & 0.284 & 0.420 & 0.527 & 0.555 & 0.686 \\  & Deviation (\%) & 1.45 & 1.77 & 2.03 & 2.48 & 2.70 & \(-\)0.23 & 3.01 & 3.33 \\ \hline \multirow{3}{*}{300} & Modal & 0.0136 & 0.0529 & 0.117 & 0.197 & 0.291 & 0.385 & 0.476 & 0.549 \\  & Spatial & 0.0134 & 0.0519 & 0.114 & 0.192 & 0.283 & 0.373 & 0.460 & 0.529 \\  & Deviation (\%) & 1.49 & 1.83 & 2.10 & 2.57 & 2.77 & 3.09 & 3.39 & 3.68 \\ \hline \multirow{3}{*}{400} & Modal & 0.0103 & 0.0399 & 0.0882 & 0.148 & 0.219 & 0.290 & 0.358 & 0.412 \\  & Spatial & 0.0101 & 0.0391 & 0.0863 & 0.144 & 0.213 & 0.281 & 0.346 & 0.397 \\  & Deviation (\%) & 1.51 & 1.85 & 2.13 & 2.61 & 2.80 & 3.12 & 3.41 & 3.70 \\ \hline \multirow{3}{*}{500} & Modal & 0.00826 & 0.0320 & 0.0707 & 0.119 & 0.176 & 0.232 & 0.287 & 0.330 \\  & Spatial & 0.00813 & 0.0314 & 0.0692 & 0.116 & 0.171 & 0.225 & 0.277 & 0.318 \\  & Deviation (\%) & 1.52 & 1.86 & 2.14 & 2.62 & 2.81 & 3.14 & 3.42 & 3.70 \\ \hline \multirow{3}{*}{600} & Modal & 0.00689 & 0.0267 & 0.0590 & 0.0991 & 0.147 & 0.193 & 0.239 & 0.275 \\  & Spatial & 0.00679 & 0.0262 & 0.0578 & 0.0965 & 0.143 & 0.187 & 0.231 & 0.265 \\  & Deviation (\%) & 1.52 & 1.86 & 2.15 & 2.63 & 2.83 & 3.15 & 3.43 & 3.71 \\ \hline \multirow{3}{*}{1000} & Modal & 0.00414 & 0.0160 & 0.0355 & 0.0596 & 0.0883 & 0.116 & 0.144 & 0.165 \\  & Spatial & 0.00408 & 0.0157 & 0.0347 & 0.0580 & 0.0858 & 0.113 & 0.139 & 0.159 \\  & Deviation (\%) & 1.53 & 1.88 & 2.16 & 2.64 & 2.83 & 3.16 & 3.44 & 3.72 \\ \hline \multirow{3}{*}{1500} & Modal & 0.00276 & 0.0107 & 0.0237 & 0.0397 & 0.0589 & 0.0775 & 0.0959 & 0.110 \\  & Spatial & 0.00272 & 0.0105 & 0.0232 & 0.0387 & 0.0572 & 0.0750 & 0.0926 & 0.106 \\  & Deviation (\%) & 1.53 & 1.88 & 2.16 & 2.65 & 2.84 & 3.16 & 3.44 & 3.72 \\ \hline \multirow{3}{*}{2000} & Modal & 0.00207 & 0.00803 & 0.0178 & 0.0298 & 0.0442 & 0.0581 & 0.0719 & 0.0826 \\  & Spatial & 0.00204 & 0.00788 & 0.0174 & 0.0290 & 0.0429 & 0.0563 & 0.0695 & 0.0795 \\ \cline{1-1}  & Deviation (\%) & 1.53 & 1.88 & 2.17 & 2.65 & 2.84 & 3.17 & 3.44 & 3.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Comparison between modal and spatial discretization. **Author Contributions:** Conceptualization, X.-D.Y. and W.Z. ; Methodology, B.-Y.X. ; Software, B.-Y.X. and Q.H. ; Formal analysis, X.-D.Y. and B.-Y.X. ; Investigation, X.-D.Y. and W.Z. ; Resources, B.-Y.X. and Q.H. ; Data curation, B.-Y.X. ; Writing--original draft preparation, B.-Y.X. ; Writing--review and editing, X.-D.Y. ; Visualization, X.-D.Y. and B.-Y.X. ; Supervision, X.-D.Y. and W.Z. ; Project administration, X.-D.Y. ; Funding acquisition, X.-D.Y. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported in part by the National Natural Science Foundation of China (Project nos.