## 3 Effect of Structural Sealant and Supporting Frame  
Compared with the main structure, the panel units of the hidden frame curtain wall are small, so the influence of the main structure on the dynamic characteristics of the panel \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline A & 5.637 & 12.134 & 15.844 & 19.158 & 26.399 & 30.088 \\ B & 6.730 & 13.833 & 18.369 & 22.310 & 28.178 & 32.663 \\ Difference(\%) & 16.241 & 12.282 & 13.746 & 14.128 & 6.313 & 7.884 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The first six-order natural frequencies identified by modal test (Hz). Figure 4: The first six measured modal shapes of panel units. If the influence of the supporting frame and structural sealant is ignored, the analytical solution of the natural frequency of a rectangular plate unit under a simply supported boundary is [21]:  
\[f_{mn}=\frac{\pi}{2}\bigg{(}\frac{m^{2}}{b_{g}{}^{2}}+\frac{n^{2}}{h_{g}{}^{2}} \bigg{)}\sqrt{\frac{D}{\rho_{\mathrm{g}}d_{g}}} \tag{1}\]  
\[D=\frac{E_{\mathrm{g}}d_{g}{}^{3}}{12(1-\mu_{g}{}^{2})} \tag{2}\]  
where \(\rho_{\mathrm{g}}\) is the density of the plate; \(b_{\mathrm{g}}\) is the width of the plate; \(h_{\mathrm{g}}\) is the height of the plate; \(d_{\mathrm{g}}\) is the thickness of the plate; \(E_{\mathrm{g}}\) is the elastic modulus of the plate; \(\mu_{\mathrm{g}}\) is the Poisson's ratio of the plate; \(m\) and \(n\) are natural numbers, taking different values for corresponding natural frequency values. For comparison, the computational results of simply supported boundary solutions are also listed in Table 4. Comparing the measured natural frequencies with calculated ones show that (a) the analytical solution of a simply supported boundary is basically the same as the numerical solution of Model 1, and the difference between two solutions is less than 1%, indicating that the mesh division of the numerical calculation model is reasonable; (b) in the case of simply supported boundary conditions, sample A has a phenomenon of partial modal repetition, which occurred in orders 2 and 3, orders 5 and 6, and orders 7 and 8. Since the panel is square, the model's rotational symmetry leads to the same natural frequency but different modes. However, for the test results, there is no repetition phenomenon, which is found under the conditions of the different cross-section of column and beam, causing the different vertical and horizontal boundary conditions of the panel. The results show that ignoring the effect of the supporting frame will result in a huge difference in the calculated natural frequencies. In order to compare the calculation errors of different models, the natural frequency obtained from the test and the finite element model are treated as an exact and approximate solution and denoted as \(r^{\star}\) and \(r\), respectively. Then, the relative error of the calculation results of the finite element model is:  
\[e=\frac{|r|-|r^{\star}|}{|r^{\star}|}\times 100\% \tag{3}\]  
Figure 6 shows the relative errors of the calculated results of finite element models of two samples. It can be seen from the calculation results that: (a) The highest error of the natural frequency obtained by a simply supported boundary can reach more than 40%, and all results of the natural frequency obtained are greater than the measured results, which indicates that ignoring the influence of structural sealant and a supporting frame will overestimate the natural frequency of panel units; (b) considering the elastic effect of structural sealant, the error from the model 2 calculation result is significantly reduced compared to the simply supported boundary, but the error can still reach more than 20%; (c) in model 3, the influence of both structural sealant and a supporting frame is considered, and most of the calculation errors are less than 5%, showing a good calculation accuracy.