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.

中文翻译：

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估算历史悠久的石砌圆顶清真寺的基本频率的经验公式

具有圆顶结构的历史石清真寺由于结构元素，材料特性，边界条件，连接方式等不同而结构复杂，因此很难建立表示这些结构真实行为的数值模型。因此，在恢复应用之前，应通过环境振动测试检查其数值模型，以进行可靠的安全评估。然而，众所周知，历史清真寺的环境振动测试非常困难且成本很高，并且需要所有者和相关政府机构的许可。本文旨在开发一种经验公式，以估计具有砌体圆顶的历史石清真寺的基本频率，以检查初始有限元模型。为此，在土耳其黑海东部地区选择了九个不同大小的石砌圆顶清真寺。通过对所选清真寺进行环境振动测试，可以确定并评估实验固有频率，振型和阻尼比。通过统计回归分析，得到了基于振动数据的石砌圆顶清真寺的基频和第二，第三频率系数的经验公式，并与控制数据进行了比较。比较结果证实了所提出的配方具有可靠的预测性能。模式形状和阻尼比已一起确定和评估。通过统计回归分析，得到了基于振动数据的石砌圆顶清真寺的基频和第二，第三频率系数的经验公式，并与控制数据进行了比较。比较结果证实了所提出的配方具有可靠的预测性能。模式形状和阻尼比已一起确定和评估。通过统计回归分析，得到了基于振动数据的石砌圆顶清真寺的基频和第二，第三频率系数的经验公式，并与控制数据进行了比较。比较结果证实了所提出的配方具有可靠的预测性能。