## 3 DDMM for Impact Resistance Calculation
### Impact Acceleration Calculation  
The design impact spectrum curve is based on the national military standard (GJB1060.1-91) [47], selecting modes with effective total mass greater than 80% of the system mass, mainly considering lower frequency modes. The propulsion shaft system's different directional modes are processed separately. The impact spectrum values vary depending on the type of ship and the equipment installation location. Based on the design impact acceleration value \(A_{\text{a}}\) and the impact velocity value \(V_{a}\), the smaller value between \(V_{a}\cdot\omega_{a}\) and \(A_{\text{a}}\) is taken as the design impact acceleration for the dynamic analysis system in the given impact direction. The values for the design impact acceleration \(A_{\text{a}}\) and impact velocity \(V_{a}\) are shown in Table 3. Since the propulsion shaft system is connected to the hull and has similar dynamic changes, the calculation is based on the benchmark acceleration and velocity of the hull components. By calculating, the impact acceleration spectrum in the three directions is obtained, as shown in Table 4, which presents some of the natural frequencies and design acceleration values. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**Longitudinal**} & \multicolumn{2}{c}{**Vertical**} & \multicolumn{2}{c}{**Transverse**} \\ \cline{2-7}  & **Frequency** & **Design Acceleration** & **Frequency** & **Design Acceleration** & **Frequency** & **Design Acceleration** \\  & **(Hz)** & **(m/s\({}^{2}\))** & **(Hz)** & **(m/s\({}^{2}\))** & **(Hz)** & **(m/s\({}^{2}\))** \\ \hline
1 & 6.327 & 38.926 & 6.564 & 100.957 & 17.319 & 261.886 \\
2 & 21.349 & 131.350 & 17.387 & 257.981 & 22.759 & 350.058 \\
3 & 25.146 & 154.705 & 21.349 & 322.577 & 38.871 & 593.228 \\
4 & 48.199 & 296.546 & 39.121 & 601.436 & 46.731 & 718.776 \\
5 & 51.030 & 309.160 & 51.709 & 791.078 & 60.354 & 927.460 \\
6 & 55.612 & 295.624 & 60.520 & 930.138 & 74.221 & 1141.618 \\
7 & 60.029 & 369.333 & 78.374 & 1205.458 & 81.133 & 1247.905 \\
8 & 81.133 & 499.172 & 87.509 & 1346.000 & 88.004 & 1353.592 \\
9 & 90.950 & 559.571 & 94.772 & 1457.701 & 91.035 & 1400.228 \\
10 & 97.222 & 598.105 & 107.616 & 1655.231 & 101.643 & 1562.395 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Propulsion shaft system longitudinal, vertical, and transverse impact acceleration values. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Impact Direction**} & \multicolumn{2}{c}{**Elastic Design**} & \multicolumn{2}{c}{**Elastic-Plastic Design**} \\ \cline{3-6}  & & \(A_{\text{a}}\) & \(V_{a}\) & \(A_{\text{a}}\) & \(V_{a}\) \\ \hline \multirow{3}{*}{hull area} & vertical & \(1.0A_{0}\) & \(1.0V_{0}\) & \(1.0A_{0}\) & \(0.5V_{0}\) \\  & transverse & \(1.0A_{0}\) & \(1.0V_{0}\) & \(1.0A_{0}\) & \(0.5V_{0}\) \\  & longitudinal & \(0.4A_{0}\) & \(0.4V_{0}\) & \(0.4A_{0}\) & \(0.2V_{0}\) \\ \hline \multirow{3}{*}{deck area} & vertical & \(0.5A_{0}\) & \(0.5V_{0}\) & \(0.5A_{0}\) & \(0.25V_{0}\) \\  & transverse & \(1.0A_{0}\) & \(1.0V_{0}\) & \(1.0A_{0}\) & \(0.5V_{0}\) \\  & longitudinal & \(0.4A_{0}\) & \(0.4V_{0}\) & \(0.4A_{0}\) & \(0.2V_{0}\) \\ \hline \multirow{3}{*}{external plate} & vertical & \(5.0A_{0}\) & \(5.0V_{0}\) & \multirow{3}{*}{not allowed} \\  & transverse & \(1.0A_{0}\) & \(1.0V_{0}\) & & \\ \cline{1-1}  & longitudinal & \(0.4A_{0}\) & \(0.4V_{0}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Design impact acceleration and impact velocity values for various installation areas.