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

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(a)

(b)

Fig. 6. Results of model updating: (a) Pareto Front of the solution for the multi-objective optimisation problem, and (b) MAC table of the compromise solution.

The results shown in Fig. 6b reveal that a good match in terms of MAC is obtained by the compromise solution, at least for the first four modes, with MAC values very close to unity. The frequencies instead, displayed in Fig. 7 together with the corresponding numerical mode shapes, present some differences from those obtained experimentally. Generally, such a discrepancy in terms of frequency can be related to several aspects which have been disregarded in the modelling, such as: the reinforced concrete frame, the boundary condition at the base of the wall opposite to the church, the presence of limestone elements, the mass of bells, etc.

f 1 =1.66 Hz (a)

f 2 =1.81 Hz (b)

f 3 =4.56 Hz (c)

f 4 =5.78 Hz (d)

Fig. 7. Numerical modes and frequencies.

5. Conclusions and future developments In this work the results of a research activity performed on the bell tower in Casertavecchia, including endoscopies, material testing on samples, Ambient Vibration testing, modal identification and model updating, are reported. The results show that the tower, even though characterised by geometrical and boundary condition asymmetry, presents two close modes at about 2 Hz. Subsequent model updating shows that multi-objective optimisation can be very useful to investigate the consistency of the model in terms of frequencies and mode shapes simultaneously, and it is possible to identify a compromise solution which fits both objectives at a given level of accuracy. Too high values of the solution discrepancy functions may highlight inconsistencies of the numerical model with the real structure, urging more specific definition of geometrical and material details.