## 4 Correctness and Rationality of ANM  
In order to validate the practicality of the analysis method (ANM), two cases were investigated in this section. In the first case, the results of the ANM were compared with the experimental results obtained by [PERSON] et al. [28]. The experimental specimen was a simply supported concrete composite beam with corrugated steel webs. The natural frequencies, calculated by ANM, of the experimental specimen in the literature were compared with the experimental results, as shown in Table 1. It was found that the natural frequencies obtained by ANM agreed well with the natural frequencies measured in the experiment in the literature. In the second case, the results of ANM were compared with results of the elementary beam theory (EBT) and the finite element method (FEM). Three simply supported abstract CBGCSWs and three fixed-support abstract CBGCSWs with different span-width ratios were investigated. Table 2 shows the geometric and material mechanical parameters of the models. According to the values of span length (\(L\)) and width (\(2b_{1}\)), the three span-width ratios were 6.72, 8.12, and 9.24. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Modal Order** & **Experimental Values** & **ANM** & **Error/\%** \\ \hline
1 & 19.203 & 18.939 & \(-\)1.375 \\
2 & 55.637 & 56.659 & 1.834 \\
3 & — & 97.084 & — \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison results of natural frequencies. The elementary beam theory (EBT), which ignores the shear lag effect, was deduced by reducing the ANM. Hence, the boundary conditions and the vibration equations of EBT were  
\[G_{e}A_{s}(w^{\prime\prime}-\theta^{\prime})-A_{p}\ddot{w}=0 \tag{51}\]  
\[G_{e}A_{s}(w^{\prime}-\theta)+E_{c}I_{c}\theta-I_{p}\ddot{\theta}=0 \tag{52}\]  
\[E_{c}I_{c}\theta^{\prime}\delta\theta\big{|}_{0}^{L}=0 \tag{53}\]  
\[G_{e}A_{s}(w^{\prime}-\theta)\delta w\big{|}_{0}^{L}=0 \tag{54}\]  
The solution of natural frequency was the same as that in Section 3. The finite element analysis software ANSYS was used to establish the above model to simulate the natural vibration characteristics (Figure 3). In the finite element model, the concrete slabs were simulated using the SOLID65 element; the corrugated webs were simulated using the SHELL43 element; the common nodes of shell element and solid element established the constraint to form the rigid connection; the beam-end simply supported boundary was simulated by constraining the transverse and vertical degrees of freedom of the beam-end nodes; the fixed-support boundary was simulated by constraining the vertical, transverse, and longitudinal degrees of freedom of beam-end nodes. In the modal analysis, the subspace method was used to extract the natural frequencies. Tables 3 and 4 show the results of EBT, ANM, and the FEM. \(e_{EBT}=\left(\text{EBT}-\text{FEM}\right)/\text{FEM}\times 100\%\) is the relative calculation error of the EBT and FEM, and \(e_{ANM}=\left(\text{ANM}-\text{FEM}\right)/\text{FEM}\times 100\%\) is the relative calculation error of the ANM and FEM, as shown in Figure 4.  
Figure 4: Relative calculation errors of the EBT, ANM, and FEM. Figure 3: Finite element model of a CBGCSW.