A Simplified Fundamental Frequency Formulation Based on In-Situ Tests for Masonry Stone Minarets

The high and slender historical masonry minarets are vulnerable to the static and dynamic loads. Performance analyses of minarets are implemented using three-dimensional numerical models in recent years. However, the complex and inhomogeneous nature of historical structures increases the likelihood of incorrect creation of numerical models. For that reason, it is important to know the experimental dynamic characteristics of masonry minarets to update the numerical models accordingly. However, it is very difficult and costly to conduct in-situ tests for every minaret. The present paper aims to develop a simplified fundamental frequency formula based on in-situ ambient vibration tests for historical masonry stone cylindrical minarets. Nineteen historical masonry stone cylindrical minarets are chosen for this purpose. Firstly, experimental frequencies, mode shapes and damping ratios of the selected minarets are determined and evaluated using the experimental measurements. Enhanced Frequency Domain Decomposition (EFDD) technique is used to obtain the experimental dynamic characteristics. Based on the obtained experimental natural frequencies, the correlation of the first natural frequency with various geometrical parameters of minaret is demonstrated by the regression analyses. In order to verify numerical models of the masonry stone cylindrical minarets, a simplified fundamental natural frequency formula based on the minaret geometrical dimensions is proposed using the experimental natural frequencies. In addition, coefficients for estimating the second and third frequencies are also presented. It has been observed that the proposed formula gives very consistent results with the measurement and literature data.