Effects of Geometrical Features on the Natural Frequencies of Historic Masonry Towers

Historic masonry towers are all around the world and play a significant role in shaping our built environment. Due to their slender shape, these towers are particularly vulnerable, as recent earthquakes have demonstrated. Many researchers have studied how these structures behave dynamically, with the aim of preserving their cultural value against the risks of damage or collapse. Lately, considerable attention has been paid to develop empirical formulas that estimate their fundamental frequency by considering geometric factors such as total height, reference base length, and effective height for constrained towers. These formulas are usually obtained using regression analysis on data from the technical literature, and so their reliability depends heavily on both the quantity and precision of available data. The variables chosen for calibrating these correlations are mainly determined by the information present in the literature; as a result, missing data can lead to underestimating the influence of some geometric aspects. To address this issue, the paper describes parametric analyses with a simplified model of masonry towers, i.e., the Euler–Bernoulli beam, aiming to show how sensitive the fundamental frequency is to different geometric and mechanical properties. These analyses show the importance of some parameters with respect to others and support the planning of experimental investigation needed for accurate predictions of a tower’s fundamental frequency.