## 4 Simulation Conditions and Procedures
### Dynamic Simulation Analysis  
Using the MATLAB simulation platform, a discrete model of the conveyor is established and the changing laws of belt tension, speed, and displacement under the non-uniform bulk material distribution are obtained through a simulation test. All the simulation cases are coded with M files in MATAB R2010b. The user interface is designed by the graphical user interface (GUI) toolbox of MATAB. When the non-uniform bulk material distribution measured by the experimental facility mentioned in Section 2.2, the real and simulated parameters of the belt conveyor are input to the GUI, the matrix of \(M\), \(C\), \(K\) in Equation (21) can be built. After a soft start control is applied on the belt conveyor, the ode 45 function in MATAB is used to solve this state equation. The computer configuration is as follows: Inter (R) Core (TM) i5-3317 U CPU @ 1.70 GHz 1.70 GHz, Memory 3.86 GB. Taking a belt conveyor at the Tongnu bulk cargo terminal of Nantong Tiansheng Gang Power Generation Co. LTD in China for example, the real parameters and simulation parameters are listed in Table 3. As described in Section 3.1, the conveyor belt at bearing segment is discretized in a very high resolution to model the changes of dynamic tension. Due to the length of belt conveyor is 4500 m and the belt speed is 3.75 m/s, 15 m as an appropriate for the unit lengths of belt at bearing segment if \(T=4\) s. The unit lengths of belt at return segment set 30 m for roughly discretized to reduce computational complexity. The value of rheological constant \(\tau\) is constant, see in description of formula (10). The conveyor belt stiffness coefficient \(k\) is the unit length of \(k_{RT}\), which is obtained from \(k_{RT}\) (formula (7)) divided by \(T\). Then multiply the conveyor belt stiffness coefficient \(k\) by rheological constant \(\tau\) to get the damping coefficient of conveyor belt \(c\). The coefficient independent of belt speed \(C_{vo}\), the coefficient related to belt speed \(C^{*}_{v}\), the unit mass of conveyor belt \(q_{\text{B}}\), the equivalent mass of upper idler \(q_{RO}\), and the equivalent mass of lower idler \(q_{RU}\) are obtained from the real parameters of the belt conveyor system. The Harrison sinusoidal acceleration curve [49] is selected to apply a soft start control on the belt conveyor. In addition, to analyze the changing rules of the dynamic behavior of the conveyor belt under the non-uniform bulk material load, three load levels, i.e., empty-load, light-load, and over-load, are set. If the non-uniform bulk material distributions on the Tongnu bulk conveyor system are measured in the field test, we could obtain more accurate simulation results of dynamic behavior of the conveyor system. However, the dynamic characteristics of a conveyor belt is so complicated that the non-uniform bulk material distribution on belt. It may cause tremendous economic loss to bulk terminal if major security incidents accidents happened, such as strip breakage or longitudinal tear. Therefore, for the safety and experimental feasibility, we perform the simulation first by setting the corresponding instantaneous material flow parameters (shown in Table 4) to analyze the belt mechanical behavior under non-uniform bulk material distribution on the belt.