## 3 Results
### Large Amplitude Vibrations of the Dry System  
It is instructive to begin the analysis by assessing the frequency-amplitude characteristic of the transient response of the dry structure. Figure 9 shows the amplitude-frequency characteristic of the vertical acceleration response at the tip of the tank computed over the first 20 periods of motion \(T1\), after the step release with a tip deformation of 2.7% of the semispan. The same characteristic is included for the wet case for reference. The frequency components that are seen to have the most significant contribution to the transient signal are found in the vicinity of the normal modes corresponding to the first two out-plane bending modes (\(F1\) and \(F2\)), first torsional mode \(F3\) and a higher-order out-plane bending mode \(F4\). These first four response components, selected by observing the amplitude of their contribution, are thus considered in the system identification process, and the corresponding frequency peaks identified in Figure 9 are named \(f_{1}\) to \(f_{4}\). Another significant feature that can be observed in Figure 9 is the evidence of sidebands appearing due to the nonlinear geometric effects that manifest themselves as additional amplitude peaks, specifically at the frequencies offset by integer multiples of one or multiple principal frequency components. In this case, evidence of the \(F1\) sidebands is immediately seen, as indicated by the amplitude peaks marked by the dashed vertical lines. Similar effects were observed in previous nonlinear studies [27]. The awareness of their presence in the shown frequency-response characteristics will be useful in the subsequent detailed analysis of the fitted response.  
While the detailed analysis of the dry system will mainly be conducted in conjunction with the wet system, consideration is also given here to the robustness of the NLS procedure introduced in Section 2 when applied to this data set. As shown in Figure 1, there are three accelerometers distributed across the length of the fuel tank. The NLS procedure is applied to the three accelerometer signals repeatedly for all three test realisations. Figure 10 shows a summary of the results that were obtained, namely the identified amplitude of component \(1\)\(A_{1}\), frequency \(f_{1}\) (in Equation (1), \(f_{j}=\omega_{j}/(2\pi)\)) and damping ratio \(\zeta_{1}\) expressed as the percentage of critical damping. The mean values among the three repetitions are shown, together with the vertical bars showing minimum/maximum deviations.  
Considering that the first component of the signal is dominated by the first modal contribution, the sensor-specific amplitude \(A_{1}\) increases in value from the tank root to the tank tip, as expected. Furthermore, the identified frequency and damping ratio (middle and bottom of Figure 10) show consistent values regardless of which accelerometer is used. The error bars decrease in size from tank root to tip as the signal-to-noise ratio increases. For the frequency component dominated by the first bending mode, it would be expected to find the same damping and frequency characteristics regardless of the accelerometer position across the tank, and this is indeed the case. The results demonstrated here are mutually consistent and indicate the robustness of the proposed identification method. Similar results were observed for the other frequency components.