Multi-body systems in waves – impact of hydrodynamic coupling on motions

Offshore installation procedures frequently require the operation of two or more structures in close proximity. Due to radiated and diffracted waves these multi-body systems are hydrodynamically coupled. As a consequence significant additional motions are observed. In case of lifting operations limitations are given by significant or maximum allowable relative motions which follow from the rigid body motions of each structure. With frequency-domain analysis the motion behaviour in harmonic waves is determined very fast and efficiently, and the resulting response amplitude operators (RAO) are used to derive operational limitations depending on seastate. Such results however have statistical character; it is not possible to derive cause-reaction chains or predict maximum motions in a deterministic wave train. With investigations in time-domain the cause-reaction chain of a multi-body system in a wave sequence can be analysed in detail and the associated hydrodynamic coupling is quantified. As direct time-domain calculations are time consuming a method of transforming frequencyinto time-domain results has been developed. This method is based on impulse response functions which are derived from the complex RAOs by Fourier transformation. Once the impulse response functions are known, the response of a structure in arbitrary wave trains can be determined by convolution. This method takes advantage of the fast frequency-domain analysis for specific time-domain investigations in deterministic wave trains, including hydrodynamic coupling as well as the influence of memory effects. With this method the interaction of hydrodynamically coupled structures in arbitrary wave sequences can be analysed in time-domain. In particular extreme situations in predefined wave trains are identified. The procedure of transforming frequency-domain results into time-domain is rarely applied in naval architecture and ocean engineering despite of its simplicity and effectiveness. As a special feature the influence of the hydrodynamic coupling can be studied in time-domain and compared to frequency-domain results.