Nonlinear Dynamic Response Analysis of Cable–Buoy Structure Under Marine Environment - Qiufu Xie; Binghan Liu; Junxian Zhang; Yaobing Zhao (Journal of Marine Science and Engineering)
The nonlinear dynamics of the cable–buoy structure in marine engineering present significant analytical challenges due to the complex motion of the buoy, which impacts the system’s dynamic response. The drag force acting on the structure can be categorized into the absolute velocity and relative velocity models, distinguished by their reference frames. The absolute velocity model incorporates flow velocity coupling terms, offering higher accuracy but at the expense of increased computational complexity. In contrast, the relative velocity model is computationally simpler and therefore more widely adopted. Nevertheless, the accuracy and applicability of these simplified models remain open to further in-depth investigation. To address these challenges, this study derives coupled differential equations for the cable–buoy structure based on the two drag force models. Galerkin discretization is then employed to construct coupled systems that account for nonlinear buoy motion, as well as decoupled systems assuming linear buoy motion. The modulation equations for the system’s primary resonance response are derived using the method of multiple scales. Numerical results indicate that changes in cable parameters lead to complex modal coupling behaviors in the system. The flow velocity coupling terms in the absolute velocity drag force model enhance the system’s damping effect, and the relative velocity drag force model, which omits these coupling terms, results in increased system response amplitudes. Although neglecting nonlinear buoy motion has little impact on the cable’s dynamic response, it significantly reduces the amplitude of the buoy’s dynamic motion. The relative velocity drag force model and the decoupled system can serve as effective simplifications for analyzing the dynamic responses of cable–buoy systems, providing a balance between computational efficiency and result accuracy. Variations in system parameters cause both qualitative and quantitative changes in the system’s nonlinear stiffness characteristics.