## 3 Transient Dynamic Simulation Analysis of Hydraulic Unit Supports
### Dynamic Simulation Analysis  
As shown in Figure 7, when a uniformly distributed impact load is applied to the top beam, the maximum stress rapidly increases to 718.41 MPa, and the maximum displacement value is 5.64 mm. After being subjected to an impact, the top beam exhibits oscillation and quickly returns to a stable condition, with the deformation amount being around 4.26 mm. A concentrated load is applied, and a stress variation nephogram of the top beam is shown in Figure 8a, with the maximum stress on the top beam significantly increasing to 950.98 MPa. Simultaneously, the maximum displacement of the top beam also increases significantly, as shown in Figure 8b, with the maximum value reaching 7.38 mm. As shown in the above analysis, the maximum deformation of the support complies with the hydraulic support design requirements, so the hydraulic unit support has high reliability in this working condition. The top beam is subjected to an eccentric impact load, and a stress variation cloud diagram of the top beam is displayed in Figure 9a. Simultaneously, the maximum displacement value of the top beam also shows a significant decrease, with the maximum value reaching 3.76 mm, as shown in Figure 9b. The results indicate that the maximum stress induced by the impact load on the side beams is much smaller than that on the  
Figure 8: Impact of concentrated load on the top beam: (**a**) concentrated load stress cloud diagram; (**b**) concentrated load displacement cloud diagram. Figure 7: Impact of the top beam under uniform load: (**a**) uniform load stress cloud image; (**b**) uniform load displacement cloud diagram. intermediate beam, with the maximum stress value reaching 468.78 MPa. When the impact load is applied to the side beam, the maximum stress at the pivot connection between the top beam and the column is 632 MPa. A stress variation cloud diagram of the top beam under torsional load is shown in Figure 10a, with the maximum stress value reaching 491.59 MPa. The maximum displacement value of the top beam also increases significantly, with the maximum value reaching 3.76 mm, as shown in Figure 10b. The results indicate that the maximum stress induced on the side beam by the impact load is much lower than that on the intermediate beam. When the load is applied to the side beam, the maximum stress value at the pivot pin connecting the top beam and the column is 328 MPa. In summary, when the top beam is subjected to concentrated loads, it undergoes maximum stress and deformation. Therefore, the structural strength of the top beam should be a primary consideration in the design of the entire support system. The simulation results indicate that when the intermediate beam and side beams are subjected to the same load impact, the stress and deformation of the intermediate beam are greater than those of the side beams. Therefore, the structural strength of the intermediate beam should be increased. Figure 10: Impact of torsional load on the top beam: (**a**) torsional load stress cloud diagram; (**b**) torsional load displacement cloud diagram. Figure 9: Impact of offset load on the top beam: (**a**) offset load stress cloud diagram; (**b**) offset load displacement cloud diagram. Figure 11 illustrates the stress and displacement of the pivot connection between the top beam and the column of the hydraulic support under the four aforementioned working conditions as the triangular wave impact load is applied, showing the variation over time. From Figure 11a, it can be seen that the maximum stress occurs at 0.5 s, with a maximum value of 954.0 MPa. Figure 11b presents the maximum displacement variation curves under different conditions, and it can be observed that the maximum displacement occurs at 0.5 s, with a maximum value of 12.35 mm. Both the maximum stress and maximum displacement closely follow the variation pattern of the triangular impact load.