## 3 Case Study
### Initial Finite Element Model  
An FE model is built with the Stabil toolbox [36]. This model will be produced before making experimental measurements to analyze the dynamic behavior of the actual structure so that the sensor grid can be arranged. The FE model uses 4-node shell elements (shell4) and beam elements (for box beam and I-beams) simultaneously (Figure 11). To be easy to control and update later, the element nodes are located at the sensor positions compared to the experiment. Details of the FE model are detailed in the following list:  
* There are 70 nodes and 69 elements that model the plate structure. In that, there are 54 shell4 elements and 15 beam elements. The cross-section of the components includes 5 types. \begin{table}
\begin{tabular}{c c c} \hline
**Mode** & **f (Hz)** & **std.f** \\ \hline
1 & 7.47 & 0.020 \\
2 & 8.62 & 0.024 \\
3 & 24.99 & 0.082 \\
4 & 36.16 & 0.112 \\
5 & 48.81 & 0.080 \\ \hline \end{tabular}
\end{table} 
Table 2: Measurement results of the plate structure. Figure 11: Type of element in FE model: (**a**) shell4; (**b**) seam. Figure 10: Five first mode shapes from the measurement: (**a**) Mode shape 1: f\({}_{1}\) = 7.47 Hz, 1 st torsion; (**b**) Mode shape 2: f\({}_{2}\) = 8.62 Hz, 1 st vertical bending; (**c**) Mode shape 3: f\({}_{3}\) = 24.99 Hz, 2 nd torsion; (**d**) Mode shape 4: f\({}_{4}\) = 36.16 Hz, 2 nd vertical bending; and (**e**) Mode shape 5: f\({}_{5}\) = 48.81 Hz, 3 rd torsion. * Primary structure: The plate under consideration is made of 0.014 m thick steel plate, strengthened by transverse stiffeners. The design documents are the basis for the FE model's material properties: the [PERSON]'s modulus of UHPC slab: Ec = 35 GPa, [PERSON]'s modulus of steel: Es = 210 GPa, concrete density \(\rho\)c = 2500 kg/m\({}^{3}\), steel density \(\rho\)s = 7850 kg/m\({}^{3}\), other nonstructural taken into account as the added volume. * Box beam and I-beam are the beam elements in the model, using the same material as the steel plate. I-beams are discontinuous: two sections of the beam with variable cross-section are built cross-section based on first-order function. * Boundary conditions: A rigid link between the plate head and the wall is built into the model by locking all DOFs of the plate structure head. In addition, according to reality, the nodes below the box girder (nodes 12, 22, 42, and 52 in the model) are considered by \"bearing\" with initial kb = 1 \(\times\) 1010 N/m stiffness. The FE model is shown in Figure 12.  
Utilizing the Block-Lanczos method, the FE model's dynamic analysis is carried out. Table 3 and Figure 13 present the first five mode shapes and frequencies. The MAC values are determined through Formula (10) between the FE model results and the actual measurements. The first 3 MAC values greater than 0.85 show good agreement between each pair of mode shapes. However, the next 2 MAC values do not reach this minimum value. The correlation between the calculated and measured mode shape vectors are not guaranteed. The frequency values are also significantly different. This is a common situation for initial FE models, most of which cannot extract modes with high accuracy. Meanwhile, depending on the calculation requirements of the structure, some structures need high accuracy for structure health monitoring, to diagnose damage, and to make major predictions. Accuracy is important for maintenance or for accurate calculations to achieve the highest efficiency in military constructions and structures. There are many  
Figure 12: Finite element model of composite plate.