Natural Frequency of Coal: Mathematical Model, Test, and Analysis on Influencing Factors

The difficulty in enhancing the low permeability of deep coal seams is the key problem restricting gas extraction. The technology of coal rock resonance and permeability enhancement excited by vibration wave is hailed as a new technology to enhance coal seam permeability. In particular, the effect of resonance and permeability enhancement is remarkable when the excitation frequency is exactly the same as the natural frequency of coal. In order to promote the application of the technology, the first step is to explore the variation characteristics of coal natural frequency and its influencing factors. In this study, two mathematical models of coal natural frequency were established, and the variations and influencing factors of coal natural frequency were discussed through an experiment on the natural frequency of coal. The results show that coal vibration has multiorder natural frequency which grows with the increase of the order. In addition, the natural frequency of coal is closely related to its elastic modulus, density, size, mass, stiffness, and other physical and mechanical parameters. The larger the coal size and mass are, the lower the natural frequency would be. The natural frequency parallel to the bedding plane is higher than that perpendicular to the bedding plane. For the saturated coal sample, moisture changes its density and reduces its elastic modulus. Consequently, its natural frequency is lower than that of the dried coal sample. The difference of organic matter and mineral content coal of different rank affects the physical and mechanical properties of coal, which leads to the difference in natural frequency of different-rank coals. The natural frequencies of different-rank coal show bituminous > anthracite > lignite. The natural frequencies of coal samples under different influencing factors are all tens of Hz. Thus, the vibration excitation of coal under the low-frequency condition is the focus of future research. The study can provide a theoretical basis for the technology of coal resonance and permeability enhancement excited by vibration wave.