Prediction of the fundamental frequencies and modal shapes of historic masonry towers by empirical equations based on experimental data

The adequate knowledge of the modal characteristics (natural frequency, modal shapes and damping) constitutes an important start point to carry out a reliable dynamic structural analysis. In the case of historic masonry towers, in particular, due to their geometric and structural characteristics they can be considered as typical and repetitive structures and predictive empirical laws can be generated. In this paper the performances of some formulas proposed in literature (even only for generic masonry towers) have been assessed on a group of case studies through the Mean Squared Error (MSE). Different results have been found for both bounded and isolated towers. Moreover, to improve to robustness and reliability of the prediction, new optimized functions, obtained minimizing the MSE of the linear regression of a model of exponential law, have been developed. The results, compared using the determination coefficient “r”, have shown a good capability of the new proposed laws to predict the fundamental frequency for the historic masonry towers. Finally, some correlation regarding the estimation of the higher modes have been highlighted.