Empirical formulation for estimating the fundamental frequency of historical stone mosques with masonry domes

Summary Historical stone mosques with masonry dome are complex structures due to their different structural elements, material properties, boundary conditions, connections, etc. It is very difficult to develop the numerical models representing the real behaviour of these structures. Therefore, their numerical models should be checked with ambient vibration tests for the reliable safety evaluations before the restoration applications. However, it is known that the ambient vibration tests of historical mosques are very difficult and costly and need permissions from the owners and relevant government agencies. The paper aims to develop an empirical formulation for estimating the fundamental frequency of historical stone mosques with masonry dome to check the initial finite element models. Nine stone mosques with masonry dome in different dimensions in the eastern Black Sea Region of Turkey were selected as examples for this purpose. By performing ambient vibration tests of the selected mosques, experimental natural frequencies, mode shapes, and damping ratios have been determined and evaluated together. An empirical formulation for the fundamental frequency and coefficients for the second and third frequencies of stone mosques with masonry dome based on vibration data are obtained by using the statistical regression analysis and verified with the control data. The comparative results confirm that the proposed formulation has a reliable predictive performance.