NONLINEAR DYNAMIC RESPONSE OF A COMPLIANT HORIZONTAL CYLINDER IN THE SPLASH ZONE

Abstract

The nonlinear dynamic behaviour of compliant offshore structures has been studied since the early 80's. Although it is well known that the behaviour of such a structure is very sensitive to the structural as well as the wave parameters, only little effort has been spent to study the behaviour in the full range of the parameter space. Therefore, the main objective of this investigation is to study the nonlinear dynamic behaviour, in a global sense, of a compliant structure subjected to wave force. A compliant horizontal cylinder subjected to wave forces in the splash zone forms the basis for the study. The cylinder is placed horizontally, perpendicular to the wave propagation direction and is allowed to move only horizontally. It is also assumed to be attached to a linear spring and damper. This arrangement gives a linear elastic structural system and the nonlinearities arise only from the external influences. The governing equation of motion is normalized and is found to be able to describe the motion when the cylinder is fully exposed, fully submerged as well as partially submerged, by adjusting the added mass according to the degree of submergence. The nonlinear dynamic behaviour of the system has been studied by using the response and bifurcation diagrams rather than time histories which are sometimes too sensitive to changes in parameter and initial condition. To facilitate the parametric study, the basic parameters have been combined in meaningful forms resulting in the definitions of the structural compliancy (CST) and structural resistivity (RST). Although no wave parameter is involved, definition of CST indicates the tendency of the structural system to remain in linear response when subjected to the inertial component of the wave force; while RST indicates the tendency of the structural system to remain undeformed when subjected to the drag component of the wave force. The response of the structural system is complex when both CST and RST are small; simpler when either one of CST or RST is large. Although CST and RST are defined for the study of the response complexities (CR's) of response diagrams for a given wave height parameter, they are found to be useful in the study of bifurcation diagrams and the global effects of wave-structure interaction. A type of qualitative change of response called period-increasing jump (PIJ) is reported. As in the case of flip bifurcation (or called period-doubling bifurcation), PIJ may occur in series called PIJ series. The change of period number associated with a PIJ is a constant; in this study, each PIJ is associated with an increase or decrease of period number by one. The reason causing PIJ to occur, is the abrupt change of the system mass due to the change of added mass when the cylinder crosses the water surface. This investigation demonstrates that by properly grouping the parameters, the behaviour of a nonlinear dynamic system in waves can be satisfactorily studied in the full range of parameter space.