Axial harmonic excitation is an emerging method for enhancing drilling speed, yet its influence on the torsional dynamics of a drill string remains unclear. To investigate these effects, this study establishes a single-degree-of-freedom (SDOF) nonlinear torsional dynamic model capable of coupling axial harmonic excitation. The model, based on Stribeck friction theory, describes the interaction by coupling the axial harmonic load with the torsional dynamic equation. After non-dimensionalizing the model, the influence patterns of static load amplitude, dynamic load amplitude, and excitation frequency on the system’s dynamics are systematically investigated. The results show that increasing the static load amplitude aggravates stick-slip vibrations, whereas increasing the dynamic load amplitude is largely ineffective for suppression and may even induce complex motions. In contrast, adjusting the excitation frequency can suppress and even eliminate stick-slip vibrations, allowing the system to achieve stable, continuous rotation. Furthermore, an interaction effect exists between the static load amplitude and the excitation frequency; at any given frequency, the Percentage of Sticking Time (PST) increases as the static load amplitude grows. This study also reveals the non-monotonic nature of the frequency’s suppression effect on vibration. These findings demonstrate that frequency optimization is the fundamental strategy for vibration suppression, requiring the dynamic load frequency to be adjusted to a specific range based on the actual weight on bit (WOB) in drilling operations. This research provides not only a deep mechanistic understanding of the drill string’s nonlinear dynamics under complex excitation but also a key theoretical basis for designing vibration suppression strategies in advanced drilling technologies.

Based on the existing research results, a theoretical fracture model of strata under the compound impact of static and harmonic dynamic load is improved, and the fracture characteristic parameters (stress intensity factor, T-stress, and fracture initiation angle) under the two far-field stress are determined according to the crack dip angle. Additionally, the effects of harmonic dynamic load on the distribution of the stress field and the fracture characteristic (the crack initiation angle, the fracture degree, the number of fracture units, and the fracture area) are further calculated and discussed by theoretical model solution, extended finite element simulation, and the secondary development of the simulation module, respectively. The research results show that the far-field stress, stress intensity factor, and T-stress vary in harmonic form with time under the compound impact of static and harmonic dynamic loads. The frequency of dynamic load affects the number of reciprocal fluctuations of stress intensity factor and T-stress as well as the crack initiation time, but has less influence on the crack initiation angle and fracture degree. While the amplitude of dynamic load affects the stress intensity factor, the extreme value of T-stress and fracture characteristics of the crack. This study has theoretical guiding significance for parameters’ optimization and realization of resonance impact drilling technology.