【目的】 煤层气废弃井中水泥塞封堵质量是防止井内污染物泄漏的关键。现行煤层气废弃井处置标准中的注水泥塞方式为简单的泥浆泵注，该方法形成的水泥塞存在水泥颗粒团聚、气泡和微孔隙等问题，导致水泥塞强度降低，易失去密封性能。【方法】 针对该问题，将振动技术应用于煤层气废弃井封堵作业中，通过专用工具带动管柱振动，依靠振动能量的传递，改变水泥浆流性以提高水泥塞封堵质量。基于Euler-Bernoulli梁理论及Hamilton变分原理，充分考虑非线性因素，建立了封堵作业中管柱−水泥浆系统三维非线性耦合振动控制模型，采用Lagrange函数和三次Hermite插值函数对管柱系统进行离散，利用Newmark-β法计算并分析了管柱在水泥浆条件下的振动特性；并搭建了机械振动试验测试平台，通过正交试验，研究了振动频率、振动时间以及振动幅值三因素在不同参数组合条件下对水泥石力学性能的影响，得到了最佳振动参数，并进一步研究了单因素对水泥石力学性能的影响规律。【结果和结论】 结果表明：(1)考虑纵横耦合效应后，管柱自身由线性结构变为非线性结构，加载使其振动固有频率明显增大，并与振型一起实时变化，在一定时间后变化呈现周期性。(2)管柱长度与振动固有频率呈反比，管柱越长其振动固有频率的变化量越小。(3)管柱−水泥浆耦合效应对振动固有频率的影响显著，在水泥浆存在的情况下，管柱系统的振动固有频率均降低，随着水泥浆密度的增加，管柱振动的固有频率降低。(4)机械振动可以使水泥浆体系更加均匀致密，表现为水泥石强度得到极大提升，当振动频率为15 Hz、振动时间为5 min，振动幅值为3 mm时，相比于未振动工况，水泥抗压强度提高38.45%、抗拉强度提高24.14%，胶结强度最大提高52.9%。研究结果可指导封堵工具振动参数的设计，为现场施工参数的确定提供参考，改善水泥浆性能以提高封堵质量，具有工程指导意义。

[Objective] The plugging quality of cement plug in abandoned coalbed methane wells is critical to preventing pollutant leakage. Current standards for handling these wells involve simple mud pump injection, which often results in cement plugs with issues like particle agglomeration, bubbles, and micropores. These defects reduce the strength of the cement plug and compromise its sealing performance. [Methods] To address this, vibration technology is applied to the plugging operation, using a specialized tool to induce vibrations in the pipe string. This process enhances the fluidity of the cement slurry via the transmission of vibration energy, thereby improving the plugging quality of the cement plug. A three-dimensional nonlinear coupling vibration control model of the pipe string-cement slurry system during plugging operations was established based on Euler-Bernoulli beam theory and the Hamilton variational principle, taking into account nonlinear factors. The Lagrange function and cubic Hermite interpolation function were used to discretize the pipe string system. The Newmark-β method was employed to calculate and analyze the vibration characteristics of the pipe string under cement slurry conditions. An experimental test platform was constructed, and orthogonal tests were conducted to study the effects of vibration frequency, vibration time, and vibration amplitude on the mechanical properties of the cement stone under various parameter combinations. Optimal vibration parameters were identified, and the influence of individual factors on the mechanical properties of the cement stone was further examined. [Results and Conclusions] The results indicate that: (1) Considering the vertical and horizontal coupling effect transforms the string from a linear to a nonlinear structure. The applied load significantly increases the natural frequency of vibration, which changes in real-time along with the vibration mode, exhibiting periodic changes over time. (2) The length of the string is inversely proportional to the natural frequency of the vibration; longer strings show smaller variations in natural frequency. (3) The coupling effect between the pipe string and the cement slurry significantly impacts the natural frequency of vibration. In the presence of cement slurry, the natural frequency of the pipe string system decreases, with higher slurry density further reducing the natural frequency. (4) Mechanical vibration enhances the uniformity and density of the cement slurry system, substantially increasing the strength of the cement stone. When the vibration frequency is 15 Hz, vibration time is 5 minutes, and vibration amplitude is 3 mm, the compressive strength of the cement increases by 38.45%, tensile strength by 24.14%, and bonding strength by 52.9% compared to non-vibration conditions. The research findings provide guidance for designing vibration parameters for plugging tools and determining field construction parameters, improving cement slurry performance to enhance plugging quality, and offering significant engineering insights.