Modeling and Analysis on Internal Resonance of a Floating Body with Dual-Anchor Cables

Floating structures are composite systems comprising multiple anchor cables and a floating body. The dynamic coupling among these components can induce complex nonlinear responses, which cause the system’s large amplitude vibration. Currently, the research focus is limited to the dynamic model with a single cable, while neglecting the indirect coupling between multiple cables such as the modal resonance. Aiming to investigate the coupling mechanism between the components, this study established a dual-cable floating-body model with consideration of the 1:1:1 internal resonance among two anchor cables and the floating body, incorporating primary resonance induced by external excitation applied to either the floating body or one of the cables. The anchor cable and floating body are coupled through the mechanical and displacement boundary conditions at the junction. Galerkin modal truncation is utilized to obtain the reduced ordinary differential equations. Asymptotic perturbation solutions are obtained by the method of multiple scales and verified by the Runge–Kutta numerical method. The results show that the vibrational energy between the cables is transmitted through the floating body; the frequency response curve of the cable exhibits multi-peak characteristics due to the modal resonance mechanism; the symmetry of the system and key structural parameters, such as the cable inclination angle and mass ratio, significantly influence the dynamic response of the cable, while having a comparatively minor effect on the floating body.