# Dynamic Analysis of an Offshore Knuckle-Boom Crane Under Different Load Applications Laws
## 5 Conclusions  
This research investigates the dynamical behavior of an offshore knuckle-boom crane, observed through modal analyses, and investigates the effect of different laws of load application. Figure 11: Variation of the maximum value of acceleration (absolute value) related to the time needed to reach the complete application of the load (\(\epsilon\)), for both configurations. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Configuration** & **Without Value of \(\epsilon=0.2\) s** & **With Value of \(\epsilon=0.2\) s** \\ \hline \multirow{4}{*}{C1} & \%\(\Delta Y_{A}=9.4975\epsilon^{-1.297}\) & \%\(\Delta Y_{A}=9.4378\epsilon^{-1.268}\) \\  & \(R_{A}^{2}=0.9744\) & \(R_{A}^{2}=0.9828\) \\ \cline{2-3}  & \%\(\Delta Y_{B}=7.4995\epsilon^{-1.255}\) & \%\(\Delta Y_{B}=7.4161\epsilon^{-1.204}\) \\  & \(R_{B}^{2}=0.9591\) & \(R^{2}=0.9526\) \\ \hline \multirow{4}{*}{C2} & \%\(\Delta Y_{A}=10.025\epsilon^{-1.223}\) & \%\(\Delta Y_{A}=9.8359\epsilon^{-1.136}\) \\  & \(R_{A}^{2}=0.9985\) & \(R_{A}^{2}=0.9493\) \\ \cline{1-1} \cline{2-3}  & \%\(\Delta Y_{B}=8.2008\epsilon^{-1.142}\) & \%\(\Delta Y_{B}=8.0549\epsilon^{-1.06}\) \\ \cline{1-1} \cline{2-3}  & \(R_{B}^{2}=0.999\) & \(R^{2}=0.9553\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Function of the regression trendline: comparison between the function without and with the value of %\(\Delta Y\) observed with \(\epsilon=0.2\) s.  
After having defined the model adopted, the material, and the most critical configurations, different modal analyses have been performed to discover the resonance frequencies of the structure in both positions analyzed. Furthermore, dynamic analyses on the load's application were carried out, considering the main variable, the amount of time needed to reach the complete application of the load, here defined as \(\epsilon\). We can summarize the key findings as follows:  
* Regarding the Y-axis displacement, the decrease of the value of \(\epsilon\) implies an increase of the overshoot related to the settling value, following a power trend line. Both the analyzed configurations display the same curve. * Regarding the accelerations along the Y-axis, even here the decrease of the value of \(\epsilon\) implies an increase of the maximum accelerations evaluated on the structure, following a power trend line. * Taking into consideration also the acceleration limit related to the gravity acceleration, it is possible to suggest a boundary condition on the so-called \(\epsilon\) time to avoid possible critical effects caused by inertial forces. Through the extrapolation of the data, it was possible to estimate the influence of the \(\epsilon\) parameter on the results, allowing for the optimization of the structure and the timing of the application and release of the load. The comprehension of accelerations' influence in these structures is crucial during the design phase, as they can result in significant effects such as inertial forces that effectively increase the payload, causing higher stresses on the crane and potentially inducing buckling. Furthermore, accelerations may cause overturning or fatigue effects due to prolonged oscillations. It must be said that this research is a preliminary study of the effect of different loading conditions on lifting equipment; therefore, it is acceptable to leave out complex phenomena that can affect the properties of the materials or the ground beneath them. Regarding the future developments, different materials are going to be adopted with the aim of lightweighting the structure, and the dynamic behavior of these new configurations is going to be studied and compared with each other. Moreover, other laws of load application can be observed, or even different load conditions, such as the wind loads or the earthquake vibrations. Conceptualization, L.S. ; methodology, L.S. ; software, I.T. ; validation, L.S. and I.T. ; formal analysis, I.T. ; investigation, L.S. ; resources, L.S. ; data curation, I.T. ; writing--original draft preparation, I.T. ; writing--review and editing, I.T. and L.S.