PSI - Issue 58

Dipendra Gautam et al. / Procedia Structural Integrity 58 (2024) 102–108 D. Gautam et al. / Structural Integrity Procedia 00 (2019) 000–000

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�� � �� �� � � �� � �

�� �� � � �� ��� �� � � �� � (1) Where �� indicates the benchmark (2019 measurement) mode shape vector and �� is the test (2023 measurement) mode shape vector. A close to 1 value of MAC indicates no damage/aggravation, whereas a lower MAC value indicates damage/aggravation due to the lack of good correlation between the mode shapes.

Fig. 1. Ananda Niketan neoclassical building in Patan, Lalitpur (inset: example of instrument setup).

3. Results and discussions An example of the detrended signal recorded on the top story of the building is shown in Fig. 2. The occasional spikes are due to the movement of people during the vibration test. From the time series records, power spectral density (PSD) plots, which indicate the power extent of the signal, were obtained for two orthogonal directions (X and Y). The PSD plots for 2019 and 2023 records are shown in Fig. 3. From the excitation PSD, �� � � and response PSD, �� � � , the squared amplitude of the frequency response function (FRF) can be obtained as: | � �| � � � �� � ��� �� ��� (2) The FRFs along the two horizontal directions (X and Y) for 2019 and 2023 measurements are plotted in Fig. 4. The figure shows that the first mode frequency for both directions is around 2 Hz for the 2023 measurement, whereas the 2019 measurement clearly shows a higher first mode frequency along Y direction. For optimal model order selection, a stabilization diagram is plotted for all measurements. An example of the stabilization plot is shown in Fig. 5. From the stabilization plot, we found model order 20 to be the appropriate model order for the vibration records. Using the same model order, modal frequencies and mode shape vectors for the first four modes were obtained. The modal frequencies are presented in Table 1.