# Vortex-Induced Vibration of Deep-Sea Mining Pipes: Analysis Using the Slicing Method
## 1 Introduction  
The deep seabed is rich in high-quality mineral resources, including essential minerals such as nickel, cobalt, copper, and manganese and other metals, which are indispensable. These resources are critical for various emerging industries, such as the development of sectors like aerospace and the production of new energy vehicles, as cited in recent studies [1, 2]. Therefore, the development of deep-sea mineral resources has become an inevitable choice for a country's future development [3, 4]. Researchers around the world have conducted a host of experiments on a variety of deep-sea mining tools and systems and have proposed a technical model with continuous and efficient mining capability, the vertical transport system (VTS) [5]. The connection between the upper hull structure and the lower underwater mining system is necessary for deep-sea mining missions, and, as such, it is often subject to a variety of factors, such as marine environmental loads, hull vibrations, and weight variations in the lower relay silo. Compared with the conventional riser fixed by hinges at both ends, the vortex-excited vibration response characteristics of the deep-sea mining pipe are more complex and are characterized by free suspension, large aspect ratios, and weak bottom constraints. Therefore, this paper investigates thevortex-excited vibration response characteristics of deep-sea mining tubes under uniform and oscillating flow variations to facilitate the understanding of the mechanism of vortex-excited vibration in deep-sea mining tubes [6; 7]. The mining system has elongated mining pipes, and the vortex-induced vibration caused by ocean currents and waves can seriously affect the safety and service life of these mining pipes during operation [8; 9; 10]. The investigation presented in this document employs a slicing method to analyze vortex-induced vibrations in deep-sea mining pipes. However, since there are fewer studies on cantilever risers, such as deep-sea mining pipes; since most of the studies are based on traditional risers with articulated restraints at both ends; and since deep-sea mining pipes have many similarities with traditional risers in terms of the appearance and materials of their physical models, the study in this paper can refer to some of the traditional risers in vortex-induced vibration. [PERSON] et al. [11] and [PERSON] et al. [12] found that the change in flow velocity leads to the change in vibration modes induced by vortex-induced vibration in marine risers. [PERSON] et al. [13] developed a sophisticated time-domain force-decomposition model designed to accurately forecast the nonlinear dynamic behaviors of risers subjected to complex, non-uniform, and non-constant flow conditions. [PERSON] et al. [14] conducted a detailed investigation into the vortex-induced vibrations of deep-sea risers subjected to bidirectional shear flows, detailing the specific amplitude and frequency responses observed under such dynamic conditions. [PERSON] et al. [15] devised a new model that incorporates the variability of tensile forces in risers that effectively delineates the dual-peaked nature of amplitude ratio curves and the patterns of vortex shedding observed. Utilizing the principles of Euler-Bernoulli and the [PERSON] wake oscillation theory, [PERSON] et al. [16] established a comprehensive governing equation for TTR VIV and explored the effects of top tension alterations on the natural vibrations within the TTR system. [PERSON] et al. [17] crafted a detailed model test scheme for assessing vortex-induced vibrations in submarine patch cords that encompasses the principles of model testing and extends to the intricate design and manufacturing processes of the patch cords, culminating in a discussion of high-level testing outcomes. In a significant contribution to the field, [PERSON] et al.