## 2 Dynamic Properties' Changes Due to the Seismic Action  
Damage-induced stiffness reduction often leads to changes in the vibration characteristics of the structural system. Consequently, tracking variations in the modal parameters over time can serve as a means to detect damage. The alterations in dynamic characteristics yield crucial information for evaluating the structural integrity of civil engineering structures. The correlation between structural damage and dynamic characteristics can be addressed by employing natural frequencies, mode shapes, and damping ratios. Following an earthquake, masonry structures typically exhibit a decrease in their natural frequencies. [PERSON] et al. [19] observed a general decrease in the statistics of natural frequencies in terms of mean, extreme, and standard deviation of a bell tower that had experienced several far-field earthquakes. The permanent frequency decays were roughly estimated to be of the order of 1-2%. [PERSON] et al. [20] record the changes of natural frequencies due to the earthquake of 4% means value for the three observed modes of 10-story reinforced-concrete building. To simulate various levels of realistic seismic damage in high rise structural buildings, [PERSON] et al. [21] conducted a series of full-scale tests on the shaking table. From the conducted studies, the authors observed the changes on natural frequencies decreasing on average 4.1, 5.4, and 11.9%. [PERSON] et al. [22] present the changes of the natural frequency of the Pizzoli town hall building during the 2016-2017 central Italy earthquake sequence from 6 to 14% for the first bending mode in x direction and 6 to 19% for the bending mode in y direction. [PERSON] et al. [23] analyze the dynamic identification results of the scale model tested of the typical Gaioleiro building subjected to several seismic test on shaking table with increasing amplitude. They recorded a first frequency change of 19% after the earthquake for the first step increase in the amplitude of 25%. [PERSON] et al. [24] noted the natural frequencies' value changes as 3.91% for transverse mode, 0.66% for longitudinal mode, and 8.69% for torsion mode, according to undamaged condition of unreinforced masonry building laboratory model. The aforementioned studies suggest that natural frequencies can be a valuable means of detecting damage and assessment to structural condition after the earthquake. While this approach is straightforward and various tools can be utilized to extract natural frequencies from experimental data, it has two inherent limitations. Firstly, it can potentially yield misleading results in terms of damage detection. Secondly, assessing damage localization becomes challenging, if not impossible, using this method. [PERSON] and [PERSON] [25] performed the research on five-story apartment buildings and the changes of natural frequencies caused by earthquakes. They concluded based on this research that the changes of natural frequencies can be significantly affected by variances in soil stiffness. On the other hand, [PERSON] et al. [26], after a strong earthquake that hit the area of Southern California, found a decrease in frequency of 12% (north-south) and 22% (east-west), which the authors attributed to minor structural damage and changes in the ground structure system caused by large earthquakes. Damage detection can be highly inaccurate if natural frequencies are used only, regardless of the associated mode shapes. Thus, researchers [27] observed the effectiveness of vibration-based methods for dynamic identification and damage detection on masonry structures using experimental tests and operational modal analysis, focusing on the entire set of modal parameters obtained from the test. As the natural frequencies of masonry buildings change due to seismic load, so do the vibration patterns. Generally, the mode shapes show the spatial distribution of displacement patterns within the structure at specific frequencies.