Numerical analysis of parametric excitation characteristics of a deep-sea mining riser under vessel heave motions

In the deep-sea mining system, the mining riser is a critical component connecting the mining vessel to the buffer station. The heave motion of the mining vessel results in varying axial forces in the riser, which may induce parametric vibration of the riser. Unlike the traditional risers with hinged ends, the mining risers with the suspended state of the bottom buffer station are more prone to parametric vibration. Prolonged exposure to parametric resonance can readily lead to fatigue damage in the riser. This study employs the characteristic root method to derive and solve the parametric resonance control equation of the mining riser. The perturbation method is used to solve the Mathieu equation and determine the parametric instability zone of the mining riser. An in-depth comparative analysis is conducted to evaluate the sensitivity and contribution of various parameters of the mining riser and traditional riser to the parametric instability zone. The results indicate that, compared to the traditional riser, the mining riser requires a lower heave frequency and amplitude to excite parametric vibration. The mass of the buffer station has the most significant impact on the parametric instability zone, whereas the damping coefficient has the least effect. The maximum vibration displacement occurs at the bottom of the riser, and the parametric resonance of the mining riser exhibits a mixed characteristic of standing wave and traveling wave behavior. Additionally, the vibrations at the bottom end of the riser demonstrate quasi-periodic characteristics.