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已有文献在计算振动固井套管固有振动特性时,未充分考虑水泥浆和套管流固耦合的影响,难以准确地得出套管在水泥浆条件下的振动特性。本文进一步考虑了套管和水泥浆的耦合振动特性,基于Euler-Bernoulli梁柱理论及Hamilton变分原理推导了套管与水泥浆耦合振动控制方程,采用有限元方法计算了套管在水泥浆条件下的振动特性,综合分析了管内压力、水泥浆密度、套管长度、水泥浆阻尼等因素对耦合系统横向振动固有频率的影响。结果表明:套管-水泥浆系统的耦合特性不可忽略,随着水泥浆密度的增加,套管横向振动的固有频率降低;套管内流体压力、水泥浆的粘性阻尼和科氏阻尼对耦合系统的横向振动固有频率影响较小,可以忽略不计;随着套管长度的增加,套管横向振动固有频率减小。研究结果可为振动发生器的优化设计提供理论基础。
In the existing literature, when calculating the natural vibration characteristics of cementing casing, the influence of fluid-structure interaction between cement slurry and casing has not been fully taken into consideration. It is difficult to accurately determine the vibration characteristics of casing under the condition of cement slurry. Based on the Euler-Bernoulli beam-column theory and the Hamilton variational principle, the coupled vibration governing equations of casing and grout are deduced. The finite element method is used to calculate the coupling vibration of casing and grout Under the vibration characteristics, the influence of the pressure in the pipe, the density of the cement slurry, the length of the casing and the slurry damping on the natural frequency of the transverse vibration of the coupled system is analyzed. The results show that the coupling characteristics of casing-grouting system can not be neglected. With the increase of grout density, the natural frequency of casing lateral vibration decreases. The fluid pressure in casing, viscous damping of grout and Coriolis damping on coupling system The natural frequency of transverse vibration has little influence, which can be neglected. With the increase of casing length, the natural frequency of casing transverse vibration decreases. The results provide a theoretical basis for the optimal design of vibration generator.