# Study on Nonlinear Vibration of Vertical Lifting Section of Bulk Grain Entrainment Ship Unloader
## 6 Conclusions  
Aiming at the stability of the lifting process of granular materials, this work constructs the vibration model of the vertical segment of the lifting process of granular materials in order to solve the problem of self-excited flutter in the process of grain vertical conveyance, which was caused by the coupling action of airflow gripping and conveyor belt traction. In this study, a nonlinear flutter method is proposed to analyze the vibration of the vertical lifting section of a bulk grain ship unloader. This study provides theoretical support for the design of pressure-supply parameters, overall structure, working operation parameters, and the early warning of the later operation, maintenance, and equipment safety of the following entrainment ship unloader. This equipment and technical support can be useful for the construction of efficient and intelligent ports.  
1. The structure of grain particles in a double-layer belt is simplified into a three-layer composite structure, and the grain material in a vertical lifting belt is laminated based on the theory of layer rationality. The nonlinear vibration differential equation of the vertical lifting section of a grain-carrying ship unloader is established by means of elastoplastic mechanics. The vibration differential equation is solved by perturbation theory and Galerkin discrete analysis.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Laminated Plate Model**} & \multicolumn{3}{c}{**Degree of Soybean Filling (k)**} \\ \cline{2-4}  & **0.1** & **0.2** & **0.3** \\ \hline Equivalent calculated values (Hz) & 0.2823 & 0.3283 & 0.2810 \\ Calculated values (Hz) & 0.5646 & 0.6566 & 0.5620 \\ Experimental values (Hz) & 0.4386 & 0.5208 & 0.4880 \\ Error (-) & 22.3\% & 20.7\% & 13.2\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Calculated and experimental values of the frequency of \(q_{1}\).  
2. The vibration response curve and natural frequency of the vertical lifting section of the bulk grain conveyor are obtained by numerical solution, and the proportion of grain in the cross section of the vertical lifting section is analyzed, that is, the effect of grain filling degree \(k\) on the vibration response and the natural frequency of the structure.
3. The experimental platform was built, and the rationality of the theoretical calculated method was verified by the experimental method, which provides a basis and reference for avoiding the occurrence of severe flutter in the conveyance process and improving conveyance efficiency.  
Methodology, M.C., M.W. and P.L.; Writing--original draft, L.Y.; Supervision, Y.L. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Training Plan of Young Backbone Teachers in Colleges and Universities in Henan Province (2020 GJS088), Opening Subject of Henan Key Laboratory of Grain and Oil Storage Construction and Safety (2021 KF-B02) and Science and Technology Research Project of Henan (No. 232102110273).  
Not applicable.  
The authors declare no conflict of interest.