Investigation on the vibration characteristics of rock based on circular plate and cylinder models: dimension, geometric shape and boundary condition

Abstract

Abstract The declaration on the “natural frequency of rock” exists in many engineering areas, and it has caused many misunderstandings. Different from the mass-spring model usually used, the circular plate and cylinder models are respectively established to clarify the relationship between the vibration characteristics (including the natural frequency and vibration mode) and their influencing factors of rock by modal analysis. The effect of the dimension, geometric shape and boundary condition on the vibration characteristics of rock with plate structure is investigated, in which the semi-analytical solutions agree well with the simulation results. By using the cylinder model based upon the Lamé–Navier equation, the effect of such influencing factors on the vibration characteristics of the block rock sample is further studied and verified by numerical simulation and experimental results. The results suggest that the natural frequency of “rock” (including the experimental rock sample) is strongly dependent on the dimension, geometric shape and boundary condition. The resonance frequency observed in the excitation experiment is not only closely associated with the natural frequency of a specific order but also dependent on the dominance of the particular vibration mode. These findings contribute to a better understanding of the rock-breaking mechanism under dynamic loads with a certain excitation frequency.