In order to study the resonance characteristics of rock under harmonic excitation, two vibration models have been presented to estimate the natural frequency of rock encountered during the drilling. The first one is a developed single-DOF model which considers the properties and dimensions of the rock. The second one is a multi-DOF model based on the principle of least action. Subsequently, the modal characteristics, as well as the influence of excitation frequency, the mechanical properties, and dimensions of the rock on its resonance frequency, are analyzed by using FEM. Finally, the ultrasonic test on artificial sandstones and materials of drill tools are carried out indoor, and the FFT transform method is adopted to obtain their resonance frequencies. Based on the analysis undertaken, it can be concluded that the natural frequency of the rock increases with the change of vibration mode. For the same kind of rock, the resonance frequency is inversely proportional to mass, while for the different kinds of rocks, the mechanical parameters, such as density, elastic modulus, and Poisson’s ratio, determine the resonance frequency of the rock together. Besides, the shape of the rock is also one of the main factors affecting its resonance frequency. At last, the theoretical research results are further verified by ultrasonic tests.

In order to study the deformation displacement and the stress field of brittle rocks under harmonic dynamic loading, a series of systematic numerical simulations are conducted in this paper. A 3D uniaxial compression simulation is carried out to calibrate and determine the property parameters of sandstone and a model of the cylindrical indenter intruding the rock is proposed to analyze the process of elastic deformation. Four main parameters are taken into account, namely the position on the rock, the frequency and the amplitude of dynamic load, the type of indenter and the loading conditions (static and static-dynamic). Based on the analysis undertaken, it can be concluded that both of the deformation displacement and stress field of the rock change in a harmonic manner under the static-dynamic loads. The frequency and the amplitude of harmonic dynamic load determine the period and the magnitude of the rock response, respectively. In addition, the existence of harmonic dynamic load can aggravate the fatigue damage of the rock and allow a reduction in static load. Our investigations confirm that the static-dynamic loads are more conducive to rock fracture than static load.

An improved model of displacement response of rock considering damping is proposed and the energy response model is further presented. Then, the rock breaking mechanism under harmonic vibro-impact is investigated based on the displacement response and energy response. Furthermore, the numerical simulations are conducted to analyze the principal stress of rock and drilling characteristics in axial and torsional directions under harmonic vibro-impact. Finally, the performance of the harmonic vibro-impact drilling technology is verified by the field application. Based on the analysis undertaken, it can be concluded that the periodic harmonic impact force makes the rock subjected to more tensile stress and continuous damage accumulation, which causes the efficient rock breakage. What’s more, the harmonic vibro-impact can also alleviate the stick-slip effect and bounce phenomenon of drill bit to a certain extent. Our investigations confirm that the harmonic vibro-impact can achieve the purpose of rate of penetration (ROP) improvement.