Mathieu-type instability of a two-point taut-moored submerged floating body under wave excitation

This paper investigates the nonlinear dynamic behaviour and parametric instability of a taut-moored submerged body subjected to waves. The analysis accounts for two key sources of nonlinearity: (i) the geometric coupling among surge, heave, and pitch motions imposed by the non-slack taut-mooring constraint, and (ii) the periodic modulation of system stiffness associated with the wave-induced variation of the constraint tension. By retaining the leading-order nonlinear terms in the geometric and tension–motion coupling, the governing equations of motion are reduced to a Mathieu-type equation. A stability analysis is then carried out using the harmonic balance method, in which the radiation damping and added mass corresponding to each harmonic and subharmonic response component are consistently incorporated. This yields a stability chart on the ω – H plane that accurately predicts the onset of Mathieu-type parametric resonance. Within the parametric resonance region, the response is dominated by a half-frequency subharmonic, whose amplitude exceeds that of the wave-frequency component. The resulting wave field exhibits pronounced higher-order features, including a significant 1.5-times-frequency component in the surface elevation. The method is further applied to a twin-tube submerged floating tunnel, confirming its applicability to engineering-scale taut-moored submerged structures.