Three-Dimensional Vibration

Abstract

The purpose of this chapter is to explore the three-dimensional vibration of an offshore platform. First, the equations of motion of the three-dimensional model are derived for two cases: a rigid structure and an elastic structure. Second, the free responses of the rigid and the elastic models are compared. The free response obtained using the rigid model allows us to gain confidence in the formulation and the numerical results obtained using the elastic model. Finally, the forced responses due to deterministic loads are investigated. Two cases are studied in particular. The first case is when a harmonic (in time) load is applied in one direction, and the second case is when steady and harmonic loads are applied in mutually perpendicular directions. The second case can be thought of as the three-dimensional loading arising from a current that also induces vortex shedding. The responses due to these simple fluid force models will prepare us for the study of responses due to more complicated fluid loading models. This subject has also been treated by Han and Benaroya [26].