# Research on the Multi-Angle Seismic Spectrum Response Law of Auxiliary Feedwater Electric Pumps
## 5 Calculations and Analyses
### Results of Analysis of Pressure-Bearing Components  
The essential pressure-bearing elements of the pump encompass the pump body, pump cover, suction section, and pump base. Any impairment to these components under seismic stress can pose substantial risks to the auxiliary feedwater electric pumps.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Order** & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \hline \(f\)**/Hz** & 41.06 & 41.09 & 171.54 & 171.6 & 242.9 & 278.18 \\ \hline \hline \end{tabular}
\end{table}
Table 2: First 6 orders of intrinsic frequency.  
Figure 8: Modal vibration patterns of auxiliary feedwater electric pumps.  
Therefore, this study meticulously delves into the seismic responses, focusing on stresses and displacements within these critical pressure-bearing elements.  
The stress and displacement distribution of the pump body is depicted in Figure 9. As shown in Figure 9a, a high-stress region is evident at the connection between the pump body's support base and the cylinder. This occurrence is attributed to a significant change in structural stiffness at this location, aligning with the actual conditions under seismic loading. This region is identified as a vulnerable area, warranting focused attention in seismic analysis. Figure 9b indicates that the overall average displacement of the pump body is relatively small. Nevertheless, there is a gradual increase in displacement from the bottom support base to the top at the inlet and outlet, attributed to minimal constraints from the inlet and outlet piping.  
Figure 10 illustrates the curves displaying the maximum stress responses for each pressure-bearing component at various angles, while Table 3 provides details regarding the angles corresponding to the occurrences of these stress maxima.  
The pump body displays considerable variability in maximum stress response under different seismic spectrum input angles. Among the pressure-bearing components, it exhibits the highest overall stress response, reaching 174.2 MPa at 45\({}^{\circ}\) and 192.9 MPa at 135\({}^{\circ}\), with a breaking point at 90\({}^{\circ}\). Conversely, the maximum stress response of the pump cover remains relatively stable, oscillating around 40 MPa. In contrast, the suction section experiences a stress peak between 0\({}^{\circ}\) and 90\({}^{\circ}\), reaching 117.1 MPa at 45\({}^{\circ}\). Between 90\({}^{\circ}\) and 180\({}^{\circ}\), especially from 120\({}^{\circ}\) to 150\({}^{\circ}\), the stress response remains nearly constant at 79.6 MPa. The pump base shows a significant stress surge between 15\({}^{\circ}\) to 30\({}^{\circ}\) and 75\({}^{\circ}\) to 90\({}^{\circ}\), reaching a pinnacle of 82.4 MPa at 135\({}^{\circ}\) while maintaining stability at 56 MPa from 30\({}^{\circ}\) to 75\({}^{\circ}\).  
Figure 11 illustrates the maximum displacement response curves of each pressure-bearing component at various angles. It is evident that the maximum displacement response for each component follows a consistent pattern. Peaks occur between 90\({}^{\circ}\) and 180\({}^{\circ}\), while troughs are observed between 0\({}^{\circ}\) and 90\({}^{\circ}\). Notably, all components reach their peaks at 135\({}^{\circ}\). However, the pump body and suction section exhibit more significant fluctuations in maximum stress response, whereas the pump cover and pump base demonstrate relatively smooth variations.  
A thorough analysis of the aforementioned data indicates that despite the consistent seismic spectrum in every input direction, the asymmetrical structure of the pump and the differing structural rigidity of its components lead to shifts in vibration frequencies. Consequently, the maximum stress and displacement responses of each pressure-bearing component vary with different input angles, displaying unique patterns of change. These observed patterns offer crucial insights for the design and installation of pertinent equipment in auxiliary feedwater electric pumps and the nuclear island. They serve as valuable reference points for future endeavors in this field.