# Research on Non-Random Vibration Analysis of Concrete Pump Truck Boom Based on Dynamic Excitation
## 3 Analysis and Simulation of Pumping Pipeline Stresses in Pump Trucks
### Discrete Element Modeling  
This study presents a discrete element model for fresh concrete developed using the Engineering Discrete Element Method (EDEM) [23], integrating particle contact theory with the material's rheological parameters, as detailed in Table 5. Table 6 lists the characteristics of the different materials. The model utilizes the Hertz-Mindlin with JKR Cohesion contact framework, proficient in precisely characterizing the visco-plastic behavior of concrete and the adhesive interactions among particles. Concrete was defined as a composite system of mortar and aggregate particles, utilizing the Jenkins-Kirchhoff-Roe (JKR) contact theory to elucidate the usual adhesion characteristics between particles [24]. Furthermore, the contact surface energy and physical property parameters are calibrated using a virtual calibration approach to guarantee that the simulation results align with the actual conditions. The model is especially appropriate for simulating the microstructure and flow characteristics of C30-grade concrete, offering a robust theoretical instrument to further optimize the concrete transport process. This study first establishes the basic range of model parameters before validating the discrete elements model for fresh concrete. To calibrate these characteristics, \"virtual experiments\" are frequently used. Figure 2 depicts the collapse experiment's procedure. The flow and extensibility of fresh concrete are measured using the collapse experiment, which also provides information about the cohesion and rheological characteristics of the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(K_{1}\) & \(K_{2}\) & \(K_{3}\) & \(K_{4}\) & \(K_{5}\) & \(K_{6}\) & \(K_{7}\) \\ \hline
0.55125 & 15,735.5 & 29,246.8 & 46,476.7 & 51,541.595 & 8147.526 & 1248.642 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Damping coefficient. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(C_{1}\) & \(C_{2}\) & \(C_{3}\) & \(C_{4}\) & \(C_{5}\) & \(C_{6}\) & \(C_{7}\) \\ \hline
0.8 & \(8\times 10^{5}\) & \(3\times 10^{4}\) & \(2\times 10^{4}\) & \(2.9\times 10^{4}\) & \(3\times 10^{3}\) & \(1.5\times 10^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Stiffness coefficient. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Typical Materials**} & **Coefficient of** & **Coefficient of** & **Collision Recovery** & **JKR Surface** \\  & **Static Friction** & **Rolling Friction** & **Coefficient** & **Energy (J/mm\({}^{2}\))** \\ \hline Coarse Aggregate–Coarse Aggregate & 0.175 & 0.15 & 0.15 & 10 \\ Coarse aggregate–Mortar & 0.2 & 0.15 & 0.05 & 3.07 \\ Coarse aggregate–Steel & 0.305 & 0.115 & 0.2 & 1.5 \\ Mortar–Mortar & 0.36 & 0.09 & 0.01 & 6.69 \\ Mortar–Steel & 0.45 & 0.425 & 0.03 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters for material interaction. material. Collapse is a significant physical characteristic of fresh concrete that can be used to describe how well it works. By measuring the concrete's collapse pattern under the influence of gravity, the experimental approach is primarily used to assess the fluidity of the material. If the simulation results of the virtual experiment and the real experimental findings are consistent within the predefined error range, then the model parameters were established in an acceptable and efficient manner. Table 7 displays the outcomes of both the real experimental materials and the simulated \"virtual experiment\" materials. This approach not only confirms the model's accuracy but also offers a foundation for additional model optimization and modification, guaranteeing the model's accuracy and usefulness in real-world engineering applications. This paper's validation experiment centers on the collapse degree, determining the model's validity by comparing the actual measured collapse degree with the simulated findings from the \"virtual experiment\". The average error of the simulated collapse degree during the validation procedure is around 3%.