Modal Analysis of Frari Historical Bell Tower in Venice: A Comparison Between Detailed and Simplified Models

In this paper a free modal analysis for the Frari historical bell tower in Venice is described. Three-dimensional finite element models and an analytical model are proposed. The proposal is to evaluate the sensitivity of the models to several geometric parameters, i.e. geometric irregularities, the presence of openings, different thicknesses of external walls. With this aim four models are proposed: i) a model of external and internal walls with real geometric parameters; ii) a model of the only external walls with real geometric parameters; iii) a simplified model of external and internal walls represented as a rectangular girder; iv) a simplified model of the only external walls represented as rectangular girder. The analytical simplified model is proposed as a comparative example. The analysis shows interesting results: i) frequencies are strongly connected to the internal nucleus; ii) mass participation is not uncoupled and always are present both flexural and torsional mode, due to geometric non-alignment to the vertical axis. Geometric irregularities entail only a part of the whole mass, which is involved in the flexural mode, while a torsional component is entailed into the mass participation. This changes entire structural behaviour. For this reasons, dynamic analysis must take into account actual geometry: effective thickness related to mass distribution, opening presence and vertical inclination.