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Evaluating the structural safety and seakeeping performance of very large floating structures (VLFS) using the rigid module flexible connector (RMFC) method remains challenging due to the complexity of the coupled hydrodynamic–structural responses in this system. In this study, a coupled hydrodynamic–structural frequency–time domain model is developed based on the RMFC method employing the planar Euler–Bernoulli beam elements to investigate the dynamic responses of multi-module floating systems. To reveal the dynamic characteristics of the systems, the coupled hydrodynamic–structural responses are investigated using a frequency–time-domain numerical model with viscous correction, in which the mass and stiffness attributes of connectors are incorporated into the system. Given the effects of hydrodynamic interaction, consideration is given to the case of three modular boxes connected by flexible beams aligned in series in shallow water to validate the present model. Higher efficiency and accuracy can be found in the system using viscous correction in potential flow theory and introducing state–space model to replace the convolution terms in the Cummins equation for the time domain. Moreover, this model can be extended to a considerable number of floating modules, which provides possibilities to analyze N-module floating systems.

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Float-over deck installation involves multi-body interactions under the wave excitations, such as the nonlinear impacts between the barge and deck via the Deck Support Units (DSUs) and between deck and substructure via the Leg Mating Unit (LMUs). These nonlinear impacts can only be analysed in the time-domain. This paper develops an efficient two-body heaving impact model based on the Cummins equation to study the nonlinear impact behaviour of float-over deck installation. In this model, the convolution term of the Cummins equation is replaced by state-space model such that the efficiency of time-domain modelling can be greatly enhanced. Both the DSUs and LMUs, serving as the shock absorbing devices, are modelled as linear compression-only springs with limited carrying capacity. When the carrying capacity of DSU and LMU is reached, direct contact between deck and barge and between deck and substructure are also modelled by using two harder compression-only springs. The established model is applied to study the nonlinear dynamics of the float-over system during the mating stage that is divided into five stages according to the percentage of deck load transferred to the substructure. Bifurcation diagram is also applied to demonstrate the nonlinear behaviour associated with the deck and barge subjected to LMU and DSU impacts. Hard impacts, namely the direct impacts between the deck and barge and between the deck and substructure, together with high frequency vibrations are found to occur at the start and end of the mating stage. The motion pattern of the deck evolving from periodic motions into chaotic motions is identified. In addition, the period-doubling phenomenon is also observed.