## 5 Analysis of Thermal Loss Results for Granular Assemblies  
Analysis of Thermal Uplift Characteristics of Granular Assemblies under Typical Vibration Conditions  
In this study, the temperature changes in 2 mm granular assemblies under five typical vibration conditions, namely, the solid-like state, micro-vibrational state, intermediate vibrational state, strong vibrational state, and gas-like state, are tested. The classification of the forced vibration state of the particles is shown in Appendix B. After being subjected to forced vibration, the particles consume energy through collisions and friction. It is generally believed that a large amount of energy dissipates as heat energy, but there is little research on this process. The changes in the surface temperature of the particles under the five typical vibration conditions over a period of 2 h are shown in Figure 5. The figure is the enlarged figure of the local surface temperature distribution of the particles taken by the infrared thermometer and the histogram of the temperature distribution of the particles in the image. The temperature distribution of the local surface of the particle is enlarged, and the color tends to be bright yellow at the higher temperature. The local surface temperature distribution amplification diagram of the particle is used to reflect the  
Figure 4: Schematic diagram of granular assemblies thermal dissipation characteristics. temperature distribution characteristics of the local temperature distribution amplification diagram of the particle. Figure 5: _Cont._  
At longer time scales, after being subjected to forced vibration, part of the energy in the particles is converted into heat through collisions and friction. Different motion states have varying effects on temperature increases. When the excitation frequency is 50 Hz and the reduced acceleration \(\Gamma\) is 0.8, the granular assemblies are in a solid-like state. From the infrared thermal images of the surface temperature changes and the corresponding temperature distribution diagrams, it can be seen that although the particles are subjected to 2 h of excitation, there is no significant change in the surface temperature of the particles. In the solid-like state, there is almost no vibration in the particles; at this time, the friction and collision effects inside the particles are not obvious, so the temperature change is also not obvious. Figure 5: Distribution of surface temperature of granular assemblies in different vibration states. (**a**) Solid-like state (the reduced acceleration is 0.8 and the excitation frequency is 50 Hz). (**b**) Micro-vibrational state (the reduced acceleration is 1.2 and the excitation frequency is 50 Hz). (**c**) Intermediate vibrational state (the reduced acceleration is 2.5 and the excitation frequency is 50 Hz). (**d**) Strong vibrational state (the reduced acceleration is 2.5 and the excitation frequency is 25 Hz). (**e**) Gas-like state (the reduced acceleration is 6 and the excitation frequency is 50 Hz). When the excitation frequency is 50 Hz and the reduced acceleration \(\Gamma\) is 1.2, the granular assemblies are in the micro-vibration state. At this time, there is no significant temperature change in the particles. During the micro-vibration process, some particles vibrate locally and rotate slightly at their positions, but this does not cause a significant change in the overall temperature. When the excitation frequency is 50 Hz and the reduced acceleration \(\Gamma\) is 2.5, the granular assemblies are in an intermediate vibrational state. For a longer period of excitation, the temperature of the particles increases slightly. According to the temperature distribution diagram of the intermediate vibrational state, there is a slight increase in the temperature of the particles. In the intermediate vibrational state, a large number of particles have small movements, and under continuous excitation, a certain amount of heat is generated in the particles.