A constant parameter time domain model for dynamic modelling of multi-body system with strong hydrodynamic interactions

Abstract

It is well known that direct evaluation of the wave-induced dynamics of floating structures by Cummins equation is time-consuming due to the convolution integrals. Particularly, for a multi-body system, a complete matrix of the impulse response functions, namely the kernel of the convolution integral in Cummins equation, is required as the cross-coupling terms in the hydrodynamic matrices are important in accurately evaluating the dynamic responses, resulting in increased computation time. Rather than solving the convolution kernel, state-space models have been adopted as an alternative, working well for single body cases. However, it has the disadvantage of numerical instability, which may cause significant errors for strongly resonant phenomena, e.g. in the multi-body interactions. To overcome this issue, the practise is to introduce a damping lid to the free surface in the gap between multiple bodies in frequency domain. Based on the hydrodynamic coefficients obtained in the frequency domain, this study presents a time domain model that combines the damping lid method and state-space model, resulting in a Constant Parameter Time Domain Model (CPTDM). Due to the nature of the time domain model, it is possible to account for nonlinear viscous damping, wherever it is appropriate. The finding shows that the damping lid method helps to stabilize the numerical simulation of the multi-body system which undergoes gap resonances. It is found that a larger damping lid factor favors the decaying of the impulse response functions and the development of lower-order state-space models. The developed CPTDM is found to work well for different wave frequencies and wave headings, with better accuracy and higher efficiency than AQWA's time-domain simulations. Particularly, at the resonant frequency, the developed CPTDM still retains good accuracy as compared with the RAO-based responses.