## 5 FE Modelling and Model Updating  
After experimental measurements and the determination of the real dynamic behaviour, a three-dimensional numerical model was created based on the finite element method (FEM) using SCIA Engineer 22.1 software [44]. The model was created according to the real geometry of the object, which was recorded with a 3D ground scanner. The load-bearing structure consists of three materials: masonry (stone blocks and lime-cement mortar), RC deck on the first floor and attic of the monastery, and wood for the roof. A detailed description of the load-bearing structure can be found in Section 2.1. Great attention was paid to the adequate modelling of all parameters affecting the dynamic properties: mass distribution, wall thickness (Figure 4b), openings, lintels, deck, stairs and roof. Secondary structural elements that are not essential to the stiffness of the model are not modelled, but their mass is added to the walls. The structure is modelled with four nodes, 2D shell elements. A mesh of finite elements of size 0.3 \(\times\) 0.3 m (31,000 elements in total) was used. Figure 15: Mode shapes of the bell tower: (**a**) 1 st mode (translation y); (**b**) 2 nd mode (translation x); (**c**) 3 rd mode (torzion z). Mindlin bending theory and direct solution method are used. The direct solution method is a standard Cholesky solution based on a decomposition of the matrix of the system. The advantage is that it can solve multiple right-hand sides simultaneously. Dynamic eigenmode analysis (determination of modal shapes and modal frequencies) is performed using subspace iteration. The subspace iteration method was introduced by [PERSON] [45] and improved by [PERSON] [46; 47]. The mass is distributed over the surface of the element [44]. Figure 16 shows the rendered numerical model (NM). For the preliminary NM, the elastic parameters of the material were adopted according to Table 2. In this model, the same quality of masonry was assumed in the church, the monastery and the bell tower. The bell cell with three bells on the top of the tower was simulated as an additional mass of 1000 kg. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Young’s Modulus E** & **Poisson Coefficient** & **Bulk Density \(\boldsymbol{\varphi}\)** \\  & **[MPa]** & \(\boldsymbol{\
u}\) & **[kN/m\({}^{3}\)]** \\ \hline Concrete & 30,000 & 0.20 & 24.5 \\ Wood & 7000 & 0.15 & 4.0 \\ Masonry & 6000 & 0.30 & 18.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Elastic material parameters of the preliminary model. Figure 16: View of the numerical model of the bell tower, the Church of St. Anthony of Padua and the Franciscan Monastery: (**a**) northeast; (**b**) northwest; (**c**) southwest; (**d**) southeast. A numerical analysis was performed to determine the modal shapes and modal frequencies. The first three modes and their dynamic properties are shown in Table 3 and Figure 17. When we compare the experimentally determined modal shapes and the numerically determined ones, we see that they agree relatively well. We see a large difference in modal frequencies due to inadequate modelling of the elastic modulus of the walls (masonry), which has a lower value than the assumed value at the bell tower, which was severely damaged in the earthquake. The recalibration was performed in an indirect way by changing the mechanical parameters of the bell tower walls (elastic modulus E and bulk density \(\varphi\)). The reduction was performed on two bell tower levels by height, as shown in Table 4 and Figure 8.  
The modal shapes and the difference between the calibrated numerical and experimental results obtained at the end of the last step are shown in Table 5 and Figure 18.