Design of natural frequency solution method based on the lateral disturbance modeling of slurry discharge pipelines in slurry shield machines

This study applies classical fluid-structure interaction (FSI) principles to analyze the lateral deflection and natural frequency of slurry discharge pipelines in slurry shield machines. By idealizing the pipeline as an infinitely long cylinder supported by equally spaced rigid rings and adopting the Euler-Bernoulli beam theory and classical fluid-structure interaction principles, the control differential equation considering the interaction between the pipeline and the flowing slurry was adapted for the tunneling environment. This model incorporates the dynamic coupling between symmetrical and asymmetrical vibration modes driven by slurry flow velocity and Coriolis force. Through analytical solutions and numerical methods, the natural frequencies and mode shapes were determined. The results show that the slurry flow will reduce the natural frequencies and may lead to system instability at high flow rates. The accuracy of the model was verified by using the measured data from the site of the South-to-North Water Diversion Project in Beijing, China, spanning four different geological strata. The relative error ranged from 1.58 to 6.29%. The results highlight the dominance of low-order modes and demonstrate that the true engineering value lies in predicting how geological conditions and slurry impurities significantly influence the pipeline's dynamic behavior, providing guiding suggestions for the engineering design and vibration control of similar systems.