## 7 Conclusions  
This study investigated the applicability of a coupled analysis method based on a substructuring technique to calculate the ISRS for a nuclear power plant structure. The model of the primary structure was condensed into an impedance function and combined with the equipment represented by an SDOF oscillator in the frequency domain. The resulting two-DOF system was used to efficiently calculate the coupled ISRS without repeated analysis of the full model. This coupled analysis method was applied to a finite element model of an auxiliary building in a nuclear power plant to validate both the accuracy and impact on the equipment response. In addition, three representative decoupling criteria to determine the acceptability of the decoupled analysis were applied to the auxiliary building to examine whether they were consistent with the coupled analysis results. The conclusions obtained from this study are summarized as follows:  
1. The acceleration and displacement response of the coupled model composed of an SDOF oscillator and a full MDOF building model matched the ISRS and primary structure displacement obtained through the two-DOF system, respectively.
2. The acceleration response around the dominant peaks in the coupled ISRS tended to decrease as the modal mass ratio between the equipment and structure increased. However, in other frequency regions, a larger mass can increase the acceleration response.
3. Even for equipment with the same mass, the response change between the coupled and decoupled analyses varies depending on the installation position and direction of motion. The response reduction was more prominent, as the deformation in the mode shape was locally concentrated within a limited region where the equipment was installed.
4. Decoupled analysis may overestimate responses significantly near the peak of ISRS and underestimate responses relatively far from the peak by more than 20% compared to the coupled analysis, although the decoupled analysis is permitted in accordance with the decoupling criteria adopted in ASCE 4-16. Therefore, the decoupling criteria need to consider the response change more directly than the natural-frequency change.
5. Decoupling criteria more conservative than ASCE/SEI 4-16 or considering the response change directly, such as US NRC or [PERSON] et al. criteria, are more adequate. In support of this, decoupling criteria defined by combining US NRC and [PERSON] et al. criteria distinguished significant response change by coupled analysis the most comprehensively in the example NPP auxiliary building analysis, and are recommended to be used.
6. An attempt to perform coupled analysis is recommended regardless of the decoupling criteria when decoupled analysis yields excessive equipment response owing to resonance with localized vibration modes.  
Conceptualization, J.-H.P.; methodology, J.-H.P.; formal analysis, S.-J.-A.; investigation, S.-J.-A.; writing --original draft preparation, S.-J.A.; writing --review and editing, J.-H.P.; supervision, J.-H.P. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry, and Energy (MOTIE) of the Republic of Korea (No. 20201510100020).  
Not applicable.  
The authors declare no conflict of interest.