PSI - Issue 44

Corrado Chisari et al. / Procedia Structural Integrity 44 (2023) 1100–1107 Corrado Chisari et al./ Structural Integrity Procedia 00 (2022) 000 – 000

1104

5

Identification of frequencies and mode shapes was performed by means of Frequency Domain Decomposition (FDD) (Brincker et al., 2001) through a purposedly developed Python/Octave script. Decimation was necessary to capture the first very close modes (Fig. 4). In particular, the first two modes were found at approximately f 1 =1.93 Hz and f 2 =2.03 Hz, corresponding to translational mode shapes in y- and x- directions, respectively. The closeness of the first two modes is rather surprising since this is an indicator of double symmetry of the building and similar stiffness distribution along the two axes. However, as previously observed, the tower presents a macroscopic asymmetrical configuration given by the presence of the nearby church as well as a large opening at the base which should produce a significant difference in translational stiffness along x and y. A simplified visualisation of the first four modes is shown in Fig. 5.

(a)

(b)

Fig. 4. Singular Value Decomposition of the Power Spectral Density for the six sensors: (a) with single decimation (Nyquist frequency 25 Hz), and (b) with double decimation (Nyquist frequency 12.5 Hz).

(a)

(b)

(c)

(d)

Fig. 5. First four modes identified by FDD.

4. Model updating by Operational Modal Analysis 4.1. The numerical model

A numerical model of the bell tower was built in the open-source FE software Code Aster (Electricité de France, 2020) with 10 node tetrahedral elements for masonry elements and concrete slab of the 3 rd sector, while the pyramidal concrete roof was modelled with bidimensional 3-node and 4-node element types. A 60-cm mesh size was adopted, and the model consisted of 69159 nodes, 43763 solid elements and 174 bidimensional elements. The model accurately reproduces the real geometry since it is based on a 3d laser scanning survey. The roof thickness was conventionally assumed equal to 5 cm. Perfect connections were considered between orthogonal walls