Application of the harmonic balance method for ship-cargo interaction with intermittent contact nonlinearities

Abstract

An important trend exhibited by the offshore wind market is the increasing size of wind turbines, leading to longer and stiffer monopiles with larger diameter-to-thickness ratios. Current transport analysis is focused on loads resulting from hydrodynamic accelerations, without taking into account the loads resulting from differences in bending deflection between the vessel and cargo. This investigation examines the structural response of a monopile and sea-fastening system subjected to displacement-based loads. The load case follows from a vessel excited using a regular wave leading to bending deflections and rigid body accelerations. The intermittent contact between the saddles and monopile is modeled by representing the saddle with a unilateral spring. This requires the use of a nonlinear solution method to obtain structural responses. The harmonic nature of hydrodynamic-based loads led to the selection of the harmonic balance method (HBM) to model the cargo-sea-fastening system. A novel understanding is gained of how cargo properties, sea-fastening properties, and sea-fastening arrangements influence the structural response of the coupled cargo-sea-fastening system. Various parametric studies are performed to identify behaviors related to the total structural response. Based on this study, the conclusion can be drawn that a large number of saddles in combination with a low stiffness is desired to minimize the structural response of the cargo and sea-fastening system. Furthermore, the influence of lashing stiffness and pretension is limited with respect to the total response. Both these conclusions also hold for an increase in cargo length and diameter.