## 5 Dynamic Analysis of the Structure
### Experimental Modal Analysis  
Due to limitations on the technical feasibility of generating a force that could induce the entire structure to vibrate, the analysis was limited to a selected structural element. Therefore, the modal analysis was carried out on a selected bar element, i.e., a column treated as a separated part elastically fixed at both ends. The tests were carried out on a group of posts located in the wall between the nave and the aisle. The two inner columns (Figure 6) and the two edge columns have a complex structure, each consisting of three branches. One branch was an element that belongs to the newer structure of the aisle (No. 1 in Figure 7). The second branch, the central one (No. 2 in Figure 7), supports the higher-situated elements of the log wall, i.e., it substitutes the logs removed here up to the ceiling level. The third branch (No. 3 in Figure 7), located on the nave side, is a framing element that reinforces the log walls on the inside of the nave. All three branches of the column stand on a single brick plinth. Branches 1 and 2 are of equal length (approximately 4.0 m) and reach the level of the ceiling of the aisle, while branch 3 (Figure 6) is longer (approximately 7.0 m) and reaches the ceiling of the nave. The column's branches are bolted together, but the level of bonding is not obvious. In order to assess the extent to which the different branches of the column cooperate, several modal analyses were carried out, differing in the directions of the applied impulse and the directions of the measured acceleration. The results of selected tests carried out are reported below. In the test labeled X13, the measurements and applied dynamic impulses followed the direction of the X-axis of the adopted coordinate system and were applied to branches 1 and 3 (Figure 8a). Figure 6: View of the wall between the nave and the aisle (own photo). Figure 8: Directions of acceleration measurements (blue) and force impulses (red) in the triple-branch column: (**a**) X13 test, (**b**) X12 test, (**c**) Y13 test. Figure 7: Column consisting of three branches in the wall between the aisle and the nave (own photo). In the second test (labeled X12), similarly to the previous test, the measurements and impulses were applied along the direction of the X-axis, but branches number 1 and number 2 were examined (Figure 8b). In the third test (named Y13), the study concerned the first and third branch, but the measurements and impulses were along the Y-axis direction (Figure 8c). The test procedure was the same for each case: a load impulse was applied at selected points on the structure with a modal hammer, and accelerations were measured at one point (the so-called base). The directions of the impulse and the measured signal were consistent in each case. Based on the recorded signals, it was possible to determine the transfer function and the coherences of the signals for each point, and an FFT could be performed. Test X13 analyzed the degree of cooperation between the first and third branches along the X-axis direction. As a result of the Fourier transform for frequencies within the range from zero to 100 Hz (Figure 9), five dominant natural frequencies were obtained. To determine the exact value of the resonant frequency, the method proposed in DewesoftX was used. This involved selecting the extremum that corresponded to the selected resonance frequency from the transfer function recorded between selected points. Then the values from the plot of the function to the right and left of the selected extremum (the so-called \"neighbouring lines\") were marked in a complex coordinate system, with the real part of the signal on the abscissa axis and the imaginary part on the ordinate axis (Nyquist plot). A circle was drawn on the system of points thus obtained, and its adjustment was carried out using the principle of minimizing error.