## 5 Analysis of Thermal Loss Results for Granular Assemblies
### Analysis of Frequency-Varying Heat Loss Characteristics of Particles  
The collision and friction between particles convert and consume energy. The experimental process of the thermal energy consumption of particles shows that the heat produced by collision and friction is a long-term energy consumption mode. Only through a longer period of collision and friction can significant thermal energy dissipation be observed. The appearance of thermal energy dissipation is closely related to the internal motion state of particles. When the particle's vibration state is in a solid-like or micro-vibrational state, less heat is produced. When the particle is in the intermediate vibrational state, strong vibrational state, or gas-like state, the particle movement is active, and the collision and friction are obvious. With the increase in time, a large amount of thermal energy will be generated. Simultaneously, the increased heat is concentrated in the interior of the particle, accumulating temperature continuously. The changes in the excitation frequency and amplitude change the motion state inside the particle, which reflects the interaction force between particles and the energy consumption process of particles.  
According to Equation (6), the frequency-variable heat loss characteristics of a 2 mm particle are as shown in Figure 8:  
Figure 8 shows the change in the thermal loss percentage of a forced-vibration particle as a function of frequency and reduced acceleration under vibration for 1 h and 2 h. As the frequency increases, the thermal loss of the particle increases. Similarly, as the reduced acceleration increases, the thermal loss of the particle decreases. In this vibration state, although particles in strong vibrational states and gas-like states are intensely vibrating  
Figure 8: Frequency-varying thermal loss percentage characteristics of granular assemblies.  
Figure 7: Frequency-varying temperature distribution of granular assemblies. (**a**) Temperature measurement location diagram. (**b**) Temperature change in granular assemblies for 1 h vibration. (**c**) Temperature change in granular assemblies for 2 h vibration.  
and have significant heating effects, the input energy to the particle is large and is mainly converted into the internal kinetic energy and potential energy of the particle. Later, frictional collisions between particles further generate thermal losses, but they are chiefly stored in the form of kinetic energy and potential energy to maintain the vibration state of the internal particle. Therefore, the thermal loss percentage is relatively small. When particles are in solid-like, micro-vibrational, and intermediate vibrational states, there is tight interaction between particles. The input energy is generally converted into the potential energy of the particle and kinetic energy resulting from micro-vibration and micro-rotation, resulting in thermal losses. At this time, the input energy is small, and the motion of the particle is not intense, so the thermal loss percentage is high. The thermal loss percentage does not exceed 70% during the energy consumption process of particle vibration. A large amount of energy may be stored in the form of the internal kinetic energy and potential energy of the particle or dissipated efficiently.