## 3 Introduction to the Generalized Inverse Cascade Method
### Optimal Intervals for Design Variables Based on Generalized Inverse Calculation Solving
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Mount** \\ **Direction** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Original** \\ **Stiffness Value** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Median Value** \\ **of Pareto Optimal** \\ **Solution Set \#1** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Median Value** \\ **of Pareto Optimal** \\ **Solution Set \#2** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **Minimum Value** \\ **of Pareto Optimal** \\ **Solution Set \#1** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **Maximum Value** \\ **of Pareto Optimal** \\ **Solution Set \#1** \\ \end{tabular} } \\ \hline \(S_{\text{FL},\text{X}}\) & 700 & 599 & 638 & 615 & 668 \\ \(S_{\text{FL},\text{Y}}\) & 4560 & 3872 & 4053 & 4096 & 3989 \\ \(S_{\text{FL},\text{Z}}\) & 956 & 860 & 816 & 890 & 877 \\ \(S_{\text{FR},\text{X}}\) & 1400 & 1182 & 1226 & 1207 & 1266 \\ \(S_{\text{FR},\text{Y}}\) & 4606 & 4179 & 4110 & 4197 & 4050 \\ \(S_{\text{FR},\text{Z}}\) & 923 & 825 & 807 & 807 & 798 \\ \(S_{\text{RR},\text{X}}\) & 1200 & 1004 & 1128 & 1120 & 1156 \\ \(S_{\text{RR},\text{Y}}\) & 800 & 716 & 681 & 696 & 749 \\ \(S_{\text{RR},\text{Z}}\) & 736 & 618 & 695 & 688 & 638 \\ Weighted force & 1385 & 1212 & 1233 & 1253 & 1235 \\ transmission rate & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Force transmission rates for the different mount stiffness values. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Mount** \\ **Direction** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Original** \\ **Stiffness Value** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Median Value** \\ **of Pareto Optimal** \\ **Solution Set \#1** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Median Value** \\ **of Pareto Optimal** \\ **Solution Set \#2** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **Minimum Value** \\ **of Pareto Optimal** \\ **Solution Set \#1** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **Maximum Value** \\ **of Pareto Optimal** \\ **Solution Set \#1** \\ \end{tabular} } \\ \hline \(X\) & 70.71 & 83.28 & 79.76 & 80.22 & 81.46 \\ \(Y\) & 74.51 & 81.75 & 83.68 & 80.11 & 78.60 \\ \(Z\) & 84.43 & 91.91 & 90.90 & 86.08 & 89.46 \\ \(\theta_{\text{x}}\) & 76.80 & 83.05 & 80.63 & 88.57 & 77.69 \\ \(\theta_{\text{y}}\) & 72.27 & 79.45 & 81.46 & 77.00 & 86.42 \\ \(\theta_{\text{z}}\) & 63.06 & 83.70 & 78.54 & 81.11 & 79.58 \\ Weighted decoupling rate & 72.26 & 83.31 & 82.20 & 81.50 & 80.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Decoupling rates of the main vibration modes for the different mount stiffness values. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Mount** \\ **Direction** \\ \end{tabular}  } & \multicolumn{2}{c}{ \begin{tabular}{c} **Original** \\ **Stiffness Value** \\ \end{tabular}  } & \multicolumn{2}{c}{ \begin{tabular}{c} **Median Value** \\ **of Pareto Optimal** \\ **Solution Set \#1** \\ \end{tabular}  } & \multicolumn{2}{c}{ \begin{tabular}{c} **Median Value** \\ **of Pareto Optimal** \\ **Solution Set \#1** \\ \end{tabular}  } & \multicolumn{2}{c}{\ \begin{tabular}{c} **Minimum Value** \\ **of Pareto Optimal** \\ **Solution Set \#1** \\ \end{tabular}  } & \multicolumn{2}{c}{ \begin{tabular}{c} **Maximum Value** \\ **of Pareto Optimal** \\ **Solution Set \#1** \\ \end{tabular}  } \\ \hline \(S_{\text{FL},\text{X}}\) & 40 & 33 & 32 & 28 & 38 \\ \(S_{\text{FL},\text{Y}}\) & 50 & 42.5 & 45 & 36 & 49 \\ \(S_{\text{FL},\text{Z}}\) & 300 & 252 & 283.5 & 233 & 271 \\ \(S_{\text{FR},\text{X}}\) & 40 & 31.5 & 34.5 & 28 & 35 \\ \(S_{\text{FR},\text{Y}}\) & 50 & 41.5 & 45 method, resulting in a significant increase in the vibration isolation performance and modal decoupling of the mount.