This paper analyzes the transverse vibration laws of 5000m ladder-shaped mining pipe under different towing velocities and accelerations in the ocean, thinking of the pipe as the beam model, discretized based on the FEM. The algorithm is used to solve the problem to obtain the transverse vibration law. The research shows that the mining pipe overall transverse vibration trend decreases first and then increases, the minimum vibration value occurs at 3000m, and the maximum occurs at the top. Increasing the towing velocity, acceleration, and ore bin weight will increase the transverse vibration value. The vibration intensity produced by the same acceleration in the constant acceleration and deceleration stages is different, and the damping effect after adding the same damping is also different. In the range of 0.01m/s²0.1m/s², the vibration reduction effect after adding damping in the constant deceleration stage is more significant, and in the range of 0.1m/s²-0.2m/s², the vibration reduction effect after adding damping in the constant acceleration stage is more significant. In the stage of the constant acceleration or deceleration, when adding the same damping, the vibration intensity generated by the large acceleration is still far greater than the vibration intensity generated by the small acceleration, so the mining ship should keep the small acceleration for towing motion.

In order to study the longitudinal vibration law of the deep sea stepped mining pipe, the pipe is regarded as the beam element and discrete by the finite element method and the mathematical model is established. Based on the Wilson-θ integration method, the numerical calculation is performed and the longitudinal vibration law under different pipe lengths, pipe thicknesses, and towing speeds is obtained. The research shows that the vibration is the irregular oscillating motion, and the law of the vibration amplitude from the top to the bottom is to decrease first and then to increase. Under the same working conditions, increasing the total length of the mining pipe, the pipe thickness, and the towing speed will reduce the amplitude of the longitudinal vibration, but only when the total length of the pipe changes, will the position of the minimum vibration amplitude be changed. The pipe thickness and the towing speed cannot change the vibration frequency, while the pipe length can change the vibration frequency. When the same external damping is added, reducing the pipe length, pipe thickness, and towing speed will increase the vibration intensity attenuation value and enhance the damping effect.