## 5 Conclusions  
1. There is a trend of increasing dominant frequencies with structural degradation (D). Our primary observation shows that the measured dominant frequencies (\(\mathrm{f_{dom}}\)) tend to increase with the growth of structural degradation (D). This phenomenon can be explained by reductions in structural rigidity due to corrosion. In accordance with the fundamental principles of structural dynamics, a decrease in structural rigidity and mass caused by corrosion leads to an increase in the natural frequency. This behaviour is consistent with the mathematical relationship described by the natural frequency formula, in which the natural \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Degradation Case** & **Spectral Power** & \
\begin{tabular}{c} **Dominant Frequency,** \\ **f\({}_{\text{dom}}\) (Hz)** \\ \end{tabular} & **Wavelet Analysis** &
\begin{tabular}{c} **FEA** \\ **Measured Frequency** \\ **f\({}_{\text{meas}}\), (Hz)** \\ \end{tabular} \\ \hline D = 0 mm & 0.3 & 0–10 s \(\rightarrow\) constant & constant & 1.384 \\ \hline D = 3 mm & 1.0 & 0 \(\
earrow\)1.35 s \(\searrow\)\(\to\) 10 s & \(\searrow\) & 1.376 \\ \hline D = 4.5 mm & 1.2 & 0 \(\to\) 4.3 s \(\
earrow\)\(\
earrow\) 7.74 s \(\searrow\)\(\to\) 10 s & \(\
earrow\) & 1.372 \\ \hline \hline \end{tabular} where: \(\rightarrow\) express constant intensity; \(\
earrow\)—increases the spectral intensity; \(\searrow\)—decreases the spectral intensity.  
\end{table} 
Table 4: Cumulative values wavelet, spectral, and FEM analysis. frequency is proportional to the square root of the stiffness and inversely proportional to the square root of the mass. In the context of corrosion, the decrease in the mass and rigidity of the structure contributes to the observed increase in the natural frequency. 2. The stability of measured frequencies under normal conditions (f\({}_{\text{meas}}\)): The frequencies measured under normal conditions (f\({}_{\text{meas}}\)) have relatively constant values, suggesting that in the absence of degradation, a structure operates in a consistent and predictable manner. This indicates that the initial structure, unaffected by corrosion, maintains the dynamic properties established during its design and construction. 3. Impact of structural degradation on dynamic behaviour: The physical interpretation of these findings reveals that structural degradation significantly influences the dynamic behaviour of the construction. The increase in dominant frequency is an indicator of the loss of rigidity and changes in structural properties. These changes can negatively affect the performance and safety of the structure, highlighting the need for periodic monitoring and preventive maintenance to prevent critical failures. 4. Role of spectral and wavelet analysis in evaluating structural behaviour: Spectral analysis and wavelet analysis play a crucial role in evaluating structural behaviour and identifying the dominant frequencies associated with different conditions of degradation or loading. Spectral analysis provides information about the power spectrum of the signal and its dominant frequencies, offering an overview of the signal's energy distribution as a function of frequency. On the other hand, wavelet analysis provides a temporal and frequency perspective of the signal, allowing the identification of significant characteristics and variations over time and frequency. 5. Including spectral and wavelet analysis results for structural health monitoring: Our results emphasise the importance of periodic monitoring and evaluations of the structure's condition to identify and address potential issues before they become critical. Integrating the results obtained from spectral analysis and wavelet analysis allows for a more comprehensive understanding of how corrosion influences structural integrity and performance. This integrated approach facilitates the development of effective maintenance and repair strategies, thereby ensuring the long-term integrity and durability of metal structures. 6.