Station keeping system for arctic floaters such as mooring cables requires an innovative engineering design coupled with a detailed investigation on its resistance against the impact loading. The ice-induced vibration, together with the wave and current actions, imposes a strong demand on the mooring cable design. However, in present industry practice, the mathematical models/software used in designing the mooring cables for offshore structures use linear strain theory. In this paper, an analytical modal based procedure for underwater submerged cable considering its geometric nonlinearity is presented. Introducing geometric nonlinearity into the modal procedure enables coupling between different modes, which is not included in the standard the linear analysis of integrated mooring system. In the present analysis, the second in-plane and first two out-of-plane modes are considered to highlight the effect of geometric nonlinearity near the 2:1 internal resonance phenomena of underwater mooring cables. The differential equation for cable is solved using a modal decomposition method considering second-order terms of the finite strain tensor. A simply supported boundary condition is assumed at both ends of the cable. A unidirectional wave loading is considered and thereby, the floater will have two translational motions, i.e., surge and heave. The floater motions will cause a support excitation at the pinned connection between the floater and mooring. This phenomenon is modelled as a base excitation at the top support point of the mooring cable. The support excitation frequency is chosen to be close to the natural frequency of the second in-plane mode. Therefore, the in-plane mode is excited directly. Ice load is applied at the support from an out-of-plane direction as a pulse load which may come from the ice impact and/or breaking. So, the out-of-plane mode is excited parametrically. It is observed that the out-of-plane mode responses show instability under certain base excitation amplitude, i.e., the responses due to the pulse load from the ice impact never decay. This instability in the responses may lead to the fatigue failure of the mooring cables. It is observed that this instability in the responses arises from the modal interaction between the different modes, i.e., autoparametric excitation, which the linear analysis is unable to capture. Numerous simulations are carried out to determine the stability boundary of different out-of-plane modes for various amplitude and excitation frequency. The stability boundaries are also determined using the harmonic balance method to verify the results obtained from the modal analysis. It can be concluded from this analysis that the nonlinear coupling terms play a significant role, close to the 2:1 resonance region which can lead to an unstable response of the mooring cables in the presence of ice loads.

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