## 3 Results
### Power Spectral Density (PSD)  
Figures 16-18 present the PSD of the four sensors (S1, S2, S3, and S4) according to the type of excitation applied. The unit measurements are reported in dB/Hz to analyze the resonant peaks and compare the PSD between the sensors and the excitation cases. The median was  
Figure 15: Scalogram image and spectral energy of S2 sensor for the ID case. calculated for all PSD data collected during each experiment to highlight dominant frequency trends and peak power levels, minimizing the influence of outliers and outlier measurements. The S1 sensor, mounted at the base of the structure, shows a spectral response that differs notably from that of the other accelerometers (S2-S4). Under ambient vibration excitations (AV and AVD cases), the power spectral density (PSD) of S1 contains several frequency peaks with amplitudes close to \(-60\) dB; in both the undamaged (AV) and damaged (AVD) states, the most prominent peak occurs at 10 Hz. Once damage is introduced, additional low-amplitude peaks appear, whose power is higher than in the undamaged (AV) configuration. This behavior indicates that S1 is especially sensitive to different frequencies once damage is present (Figure 16). For the transient excitations (ID and IH cases), the spectrum recorded by S1 is broadly similar to that of S2, but two key differences arise. (i) The peak at 5.23 Hz, close to the second natural frequency, is more pronounced in S1. (ii) The power of frequency components are below \(-40\) dB compared to the other sensors, possibly because S1 is mounted directly on the rigid base (Figure 17). In the harmonic excitations (\(f_{d1}\), \(f_{d2}\), and \(f_{d3}\) cases), the shaker is attached directly to the base of the structure; therefore, S1 is dominated by the forcing frequency \(f_{di}\) and its harmonics (\(2f_{di},3f_{di},\ldots,nf_{di}\)). Consequently, the sensor provides little useful information for identifying the structure's resonance frequencies in these tests (Figure 18). Although S1 can reveal changes in spectral content under the different excitation scenarios, particularly under ambient vibration and transient excitations, its location at the base limits the identification of resonance frequencies relative to the other sensors. Figure 16 shows that the AVD case produces higher spectral power in most frequency components than the AV case. However, at 9.32 Hz, the AV excitation yields the highest power peak across sensors S2, S3, and S4. Figure 17 shows that the IH case produces higher spectral power in most frequency components than the ID case. However, at 1.80 Hz, the ID excitation yields the highest power peak across all sensors. Figure 18 presents the vibration response of the 3-DoF structure under shaker excitations with three frequency values (\(f_{d1}\), \(f_{d2}\), and \(f_{d3}\)). In each spectrum, the dominant peaks occur at the excitation frequency and its harmonic components. In general, the spectral power of the corresponding natural frequency peaks of the system (\(f_{n1},f_{n2},f_{n3}\)) are observed to be more attenuated compared to their respective excitation frequencies and harmonics for sensors S2, S3, and S4, indicating that the resonance amplification is limited to the chosen excitation levels. However, under excitation at \(f_{d3}\) with sensors S2, S3, and S4, the component closest to the first natural frequency (\(\approx 1.8 Hz\)) shows higher power than those close to \(f_{n2}\) and \(f_{n3}\). This response occurs because \(f_{d3}\) is sufficiently distant from all resonant frequencies. Table 3 indicates that the AVD, ID, and IH cases have the same resonance frequencies but with different power magnitudes. The highest power peaks in the spectrum for frequencies of 1.80 Hz, 5.72 Hz, and 9.32 Hz were recorded by the S3 sensor for the first and third frequencies and S2 for the other frequencies. However, there is a clear difference between the values of these frequencies in the AV case, which corresponds to when the structure does not present any damage.