Vibro-Impact Drilling (VID) is a promising efficient rock-breaking technology in hard-rock drilling. This technology is designed to break rock with vibration or impact loads and its ultimate goal is to break rock in resonance state. Characteristics of viscosity and density have a significant influence on the realization of rock resonance. So a rock response model with fractional damper is established and the rock micro-vibration equation based on the model is obtained. Then the dynamic mechanic parameters and the resonance response of the rock under periodic non-harmonic excitation are presented. Finally, simulation is conducted to verify the model. It is confirmed that the introduction of fractional viscosity term can better reflect the dynamic characteristics of the rock. The maximum vibration displacement of the rock can be obtained when the excitation frequency is appropriate and the viscosity characteristic reduces not only the frequency, but also the intensity of the rock resonance. The natural frequency of rock decreases with the increase of the density, while the density has positive effect on the intensity of the rock resonance. The vibration response of the rock is also related to the impact parameters. The research of this paper is of great significance to the development of VID technology and the design of Vibro-Impact tools.

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