## 6 Conclusions  
In this study, the physical meaning of the time-domain elastic seismic response spectra was analyzed, and the generation process of the response spectra was described. First, we analyzed the research object and the calculation principle of time-domain elastic seismic response spectra. The time-domain seismic response spectrum was transformed into the time-domain seismic response spectral matrix. We described the specific process of the matrix formation and the self-developed calculation program for the time-domain elastic seismic response matrix for any seismic wave (curved surface of the response spectrum). Finally, the calculation method for the dynamic seismic response of the structure was introduced by applying time-domain mode decomposition to the response spectral matrix. The results obtained made it possible to draw the following conclusions.  
1. The time-domain seismic response spectra are the values of the seismic influence coefficient at the time \(t\) of an earthquake for a single-degree-of-freedom and natural vibration period \(T_{c}\). The natural vibration period \(T_{c}\) is plotted on the \(Y\)-axis, time \(t\) is plotted on the \(X\)-axis, and the seismic influence coefficient \(\alpha\)(\(x\),\(y\)) on the \(Z\)-axis. The seismic response analysis based on the time-domain seismic response spectra yielded the maximum response of the structure and the seismic response simultaneously occurring for different vibration modes at each time point.
2. The time-domain mode decomposition not only considered the maximum seismic response of each vibration mode but also included the seismic response of different vibration modes at each time point. Thus, it quantified the dynamic time history of the structure's seismic response through the seismic response's time-domain spectra.
3. Through comparative analysis, the calculation accuracy of the time-domain response spectrum can meet the engineering requirements, and the calculation efficiency is significantly higher than that of the elastic dynamic time-history method.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Standard Mode** & **Time-Domain Mode** & **Elastic Dynamic Time** \\
**Results** & **Response Spectrum Method** & **Response Spectrum Method** & **Method** \\ \hline Maximum horizontal base & 1242.7 kN & 1236.4 kN & 1268.9 kN \\ seismic shear & & & \\ \hline Time when the maximum & & at the 122 nd second & at the 142 nd second \\ value occurs & & & \\ \hline Calculation duration & 1 min 12 s & 2 min 42 s & 8 min 53 s \\ \hline \hline \end{tabular}
\end{table}
Table 1: Calculation and analysis of base shear force for a frame structure.  
**Author Contributions:** Conceptualization, Q.L.; methodology, Q.L. and C.Z.; software, Q.L.; validation, Q.L. and J.H.; formal analysis, Q.L.; investigation, Q.L.; resources, J.H. and H.Z.; data curation, Q.L.; writing--original draft, Q.L.; writing--review and editing, Q.L. and C.Z.; visualization, Q.L.; supervision, C.Z.; project administration, C.Z. and J.H.; funding acquisition, J.H. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This study was supported by the National Natural Science Foundation of China (51968019, 51408312), the High-level talent project of Hainan basic and applied basic research plan (2019 RC148, 2019 RC351), the Natural Science Foundation of Jiangsu Province (BK20130982), the \"Nanhai Series\" Yucai Program (Document no. 21 of Hainan Talent Office, 2019), and the characteristic innovation(Natural Science) projects of scientific research platforms and scientific research projects of Guangdong Universities in 2021.  
**Conflicts of Interest:** The authors declare no conflict of interest.