The theory of non-linear elastic ship-water interaction dynamics

Non-linear mathematical models are developed to provide formulations of the equations of motion describing the dynamical interaction behaviour between an incompressible or compressible ideal fluid and a moving or fixed, elast ic or rigid structure. The general theoretical approach is based on the fun damental equations of continuum mechanics, the concept of Hamilton's princi ple and suitably formulated variational principles. The resultant mathemati cal model expressed in a fixed or a moving frame of reference, allows the t heoretical establishment of non-linear problems associated with ship dynami cs and offshore engineering. Through applications of the variational princi ples, this is demonstrated by rigorously deriving the governing equations o f motion for general non-linear ship-water interaction problems. In particu lar, the theory is applied to a rigid ship travelling in calm water or in w aves, a bottom-fixed rigid rod or tower excited by an incident wave and a t wo-dimensional elastic beam travelling in waves. (C) 2000 Academic Press.