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, elastic or rigid structure. The general theoretical approach is based on the fundamental equations of continuum mechanics, the concept of Hamiltonʹs principle and suitably formulated variational principles. The resultant mathematical model, expressed in a fixed or a moving frame of reference, allows the theoretical establishment of non-linear problems associated with ship dynamics and offshore engineering. Through applications of the variational principles, this is demonstrated by rigorously deriving the governing equations of motion for general non-linear ship-water interaction problems. In particular, the theory is applied to a rigid ship travelling in calm water or in waves, a bottom-fixed rigid rod or tower excited by an incident wave and a two-dimensional elastic beam travelling in waves.