Drilling tool vibration failures occur frequently in the southern Sichuan shale gas field, primarily as damage to measurement while drilling (MWD) systems and steering mechanisms. These failures significantly hinder the safe and cost-effective development of shale gas resources. To mitigate tool failures caused by drilling vibrations, the vibration characteristics of static push-the-bit rotary steering tools during inclination-holding operations were investigated. A multi-scale coupled dynamics model, integrating ADAMS and ABAQUS, was established and combined with real-time downhole vibration monitoring data. A comprehensive evaluation system was developed that incorporates both microscopic resonance characteristics and macroscopic vibration parameters. The results show that the maximum vibration frequency, displacement, stress, and acceleration are concentrated at the contact interfaces between the bottom hole assembly (BHA) and the wellbore, indicating a spatial energy aggregation effect at these points. Resonance is rarely observed during BHA operations, and vibration stresses remain well below the yield strength of the drill pipe. However, excessive vibration acceleration beyond operational limits is identified as the primary failure mechanism. Parameters such as weight on bit (WOB), shock sub configuration, and upper stabilizer placement influence vibration intensity, while torque variation exerts the most significant overall impact. Based on these findings, a dual-factor control chart was developed to relate drilling parameters with vibration acceleration thresholds, providing theoretical guidance for parameter optimization. This approach addresses the common field practice of indiscriminate parameter reduction in response to vibration. Field applications show a 23% increase in drilling speed compared with baseline operations, confirming the effectiveness of the proposed dynamic vibration control strategy. The research results establish a theoretical basis for vibration mitigation in complex shale gas drilling and offer practical solutions to enhance performance.