Analysis of natural frequency of deep-sea mining beam riser considering mixing pump

In this study, the Euler-Bernoulli beam was used to calculate the mining riser under variable tension by considering the riser as a beam vibration problem. The natural frequency and mode shape of the mining riser are investigated based on the Wentzel-Kramers-Brillouin (WKB) method. The influence of different mixing pump masses and positions is calculated using a continuous function. The bottom boundary condition of the mining riser is also considered in the calculation. The calculation results show that when the hinged boundary condition at both ends changes to a horizontal-free condition at the bottom, the natural frequencies decrease. When considering the effect of the mixing pump, note that the larger the mass of the mixing pump, the greater the increase in the natural frequency of the riser. The magnitude of increase becomes more evident as the mode grows. Furthermore, the closer the position of the mixing pump to the bottom, the higher the natural frequency. The eigenfunction is also deflected at the mixing pump position.