## 3 Experimental Results, Analysis and Discussion
### Detection of Failing Joint
Values for this quantity are quite low (ranging from 0.17 to 0.43 dB per parameter) and indicate successful approximation. Furthermore, an additional remark on the standard deviation of the spectra presented in Figure 3b may be formulated. In fact, the upper and lower limits of the curves presented in Figure 3b (corresponding to the confidence intervals for those curves at 95% level) indicate that there are quite small differences of up to \(\pm\)1.3 dB, for peak magnitudes generally ranging between \(-\)75 and \(-\)80 dB. These narrow intervals suggest that it is reasonable to estimate damping factor values by applying the second order approximation to power spectrum curves such as those in Figure 3b. The same remarks are valid for tests with structure-B, again with data exhibiting significant noise and total harmonic distortion characteristics (with relevant values between 13.75% and 27.74% for 50 harmonics estimated with test data from cases in Table 2). Figure 4a presents the frequency characteristics of structure-B for the configurations described in Table 1, with the exciter driven by a triangular signal with amplitude of 600 mVpp and frequency of 80 Hz. Again, structure-B with normally secured joints produces data with peaks at higher frequencies than those from slabs with failing joints. The exact values of frequencies and the associated damping values estimated by means of the second-order approximation may be found in Table 2. Focus is now given on the two largest peaks of the spectrum plot, since the third and fourth peaks are roughly of equivalent magnitude. This property of shifted frequencies is consistent for the two largest peaks (modes) in the power spectrum plot, but a trend opposite to that shown in Figure 3b is noted. Data from structures with failing joints have modes at _lower_ frequencies than data from structures with normally fixed joints, unlike what is observed in Figure 3b. Since this could create doubts about a poorly executed set of test runs and/or some inappropriate setting, another set of test runs now with the exciter driven by a triangular signal at 80 Hz but with an amplitude of 800 mVpp was conducted. Again, data exhibited significant noise and total harmonic distortion characteristics (with relevant values between 20.97% and 26.87% for 50 harmonics estimated with test data from cases in Table 3). Results proved very similar to \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Test Case—Run \#**} & \multicolumn{2}{c}{**Mode—I**} & \multicolumn{2}{c}{**Mode—II**} & \multicolumn{2}{c}{**Mode—III**} \\ \cline{2-7}  & \(\mathbf{\zeta}\) & \(\mathbf{\omega n}\)**(Hz)** & \(\mathbf{\zeta}\) & \(\mathbf{\omega n}\)**(Hz)** & \(\mathbf{\zeta}\) & \(\mathbf{\omega n}\)**(Hz)** \\ \hline NJ-A \#1 & \(6.28\times 10^{-4}\) & 1224 & \(7.85\times 10^{-4}\) & 1412.5 & \(2.37\times 10^{-4}\) & 1601.5 \\ NJ-A \#2 & \(2.91\times 10^{-4}\) & 1217.5 & \(4.62\times 10^{-4}\) & 1406.25 & \(4.98\times 10^{-4}\) & 1595.1 \\ NJ-A \#3 & \(7.35\times 10^{-4}\) & 1211 & \(7.49\times 10^{-4}\) & 1399.7 & \(5.92\times 10^{-4}\) & 1588.5 \\ FJ1-A \#1 & \(2.49\times 10^{-4}\) & 1269.6 & \(1.83\times 10^{-4}\) & 1464.5 & \(2.98\times 10^{-4}\) & 1660 \\ FJ1-A \#2 & \(3.18\times 10^{-4}\) & 1244 & \(3.85\times 10^{-4}\) & 1438.8 & \(9.94\times 10^{-5}\) & 1629.1 \\ FJ1-A \#3 & \(1.63\times 10^{-4}\) & 1230.5 & \(1.26\times 10^{-4}\) & 1419.3 & \(2.38\times 10^{-5}\) & 1614.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Testing scenarios (at 80 Hz–600 mVpp) for detecting failing joints in structure-A. those already available (obtained with the exciter driven at 600 mVpp) and may be seen in Figure 4b. The exact values of frequencies and the associated damping values estimated by means of the second-order approximation may be found in Table 3. In all runs, values for \(\surd r(k)/q\) (see Section 2.3--step 3) range between 0.19 and 0.46, thus indicating successful approximation of the considered spectra.