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 Hamilton's 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.

[1]  W. G. Price,et al.  Fundamental viscous solutions or 'transient oseenlets’ associated with a body manoeuvring in a viscous fluid , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[2]  W. G. Price,et al.  On the use of Equilibrium Axes and Body Axes in the Dynamics of a Rigid Ship , 1981 .

[3]  T. Francis Ogilvie,et al.  Singular-Perturbation Problems in Ship Hydrodynamics , 1970 .

[4]  J V Wehausen,et al.  THE MOTION OF FLOATING BODIES , 1971 .

[5]  K. Washizu.  Variational Methods in Elasticity and Plasticity , 1982 .

[6]  R. G. Lerner,et al.  Encyclopedia of Physics , 1990 .

[7]  S. C. Hunter,et al.  Mechanics of Continuous Media , 1977 .

[8]  J. Oden,et al.  Variational Methods in Theoretical Mechanics , 1976 .

[9]  Job J.M. Baar,et al.  A three-dimensional linear analysis of steady ship motion in deep water , 1986 .

[10]  Odd M. Faltinsen,et al.  Sea loads on ships and offshore structures , 1990 .

[11]  Leonard Meirovitch,et al.  Methods of analytical dynamics , 1970 .

[12]  J. N. Newman.  The Theory of Ship Motions , 1979 .

[13]  M. Isaacson,et al.  TIME-DOMAIN SECOND-ORDER WAVE RADIATION IN TWO-DIMENSIONS , 1993 .

[14]  John V. Wehausen,et al.  THE WAVE RESISTANCE OF SHIPS , 1973 .

[15]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[16]  W. G. Price,et al.  Hydroelasticity of Ships , 1980 .

[17]  G. X. Wu,et al.  Hydrodynamic forces on submerged oscillating cylinders at forward speed , 1987, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[18]  Chiang C. Mei,et al.  NUMERICAL METHODS IN WATER-WAVE DIFFRACTION AND RADIATION , 1978 .

[19]  R. L. Seliger,et al.  Variational principles in continuum mechanics , 1968, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[20]  Edward V. Lewis,et al.  Principles of naval architecture , 1988 .

[21]  R. Bishop,et al.  A general linear hydroelasticity theory of floating structures moving in a seaway , 1986, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[22]  Michael Isaacson,et al.  TIME-DOMAIN SECOND-ORDER WAVE DIFFRACTION IN THREE-DIMENSIONS , 1992 .

[23]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[24]  N. Barltrop,et al.  Dynamics of Fixed Marine Structures , 1991 .

[25]  W. G. Price,et al.  A mixed finite element method for the dynamic analysis of coupled fluid–solid interaction problems , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[26]  W. G. Price,et al.  Mixed finite element substructure—subdomain methods for the dynamical analysis of coupled fluid-solid interaction problems , 1996, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[27]  Poul Andersen,et al.  Hydrodynamics of Ship Propellers , 1993 .

[28]  R. Ohayon,et al.  Fluid-Structure Interaction: Applied Numerical Methods , 1995 .

[29]  Antony Jameson,et al.  Fast multigrid method for solving incompressible hydrodynamic problems with free surfaces , 1993 .

[30]  L. C. Woods,et al.  The thermodynamics of fluid systems , by L. C. Woods. Pp 359. £12·50. 1985. ISBN 0-19-856180-6 (Oxford University Press) , 1987, The Mathematical Gazette.

[31]  James Serrin,et al.  Mathematical Principles of Classical Fluid Mechanics , 1959 .

[32]  R. Eatock Taylor,et al.  Radiation and diffraction of water waves by a submerged sphere at forward speed , 1988, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[33]  Touvia Miloh,et al.  Hamilton’s Principle, Lagrange’s Method, and Ship Motion Theory , 1984 .