Three dimensional transient analysis of the instal

电线电缆网 > 技术资料共享 > Three dimensional transient analysis of the instal（完整版）

Three dimensional transient analysis of the instal - 无图版

绿野仙踪 --- 2007-12-06 08:37:42
1

Three dimensional transient analysis of the installation of marine cables

M. A. Vaz¹, J. A. Witz² and M. H. Patel²

(1)	Present address: Laboratory for Submarine Technology, Ocean Engineering Program, COPPE, Federal University of Rio de Janeiro, 21941-590 Rio de Janeiro, Brazil

(2)	Present address: Santa Fe Laboratory for Offshore Engineering, Department of Mechanical Engineering, University College London, London, UK

Received: 25 March 1996 Revised: 16 September 1996

Summary A numerical solution for the three dimensional transient motion of a marine cable during installation is presented for the case of a cable laying vessel arbitrarily chaning speed and direction while paying out cable with seabed slack. The cable transient behaviour is governed by the numerical solution of a set of non-linear partial differential equations with the solution methodology incorporating both spatial and temporal integration. The space integration is carried out by dividing the cable inton straight elements with equilibrium relationships and geometric compatibility equations satisfied for each element. The position of each element is described by its elevation and azimuth angles and, therefore, a system of 2n non-linear ordinary differential equations is established. The time integration of this set of equations is performed using a high order Runge-Kutta technique. Results are presented fro the cable tension and element elevation and azimuth angles as functions of time and for transient cable geometries when the cable ship executes horizontal planar manoeuvres.</DIV><DIV class=Keyword>List of symbols A _t, A_n, A_b tangential, normal and binormal components of cable element acceleration vector - A _c(s, t) cable element acceleration vector - C _D,C _f normal and tangential friction drag coefficients - C _m added mass coefficient - D _nn,D _bb,D _tt normal, binormal and tangential drag forces - d cable diameter - G _i(t) constant of integration - g gravitational acceleration - H hydrodynamic constant of the cable - I, J, K inertial system unit vectors - i, j, k tow vessel system unit vectors - L _i length of the cable element - N, B, T normal, binormal and tangential node forces - n number of straight elements - 2N _i/L _i, 2B _i/L _i geometric stiffness terms - OXYZ inertial system - oxyz system attached to the tow vessel - o prime

local system - R _c(s, t) vector position of a cable element - r _o(t),r _c(s, t) ship and cable element position vectors - $\frac{\partial }{{\partial t}}r_c \left( {s, t} \right)$ cable element velocity vector - $\frac{{\partial ^2 }}{{\partial t^2 }}r_c \left( {s, t} \right)$ cable element acceleration vector - $\frac{d}{{dt}}r_0 \left( t \right) = - \frac{d}{{dt}}x_0 \left( t \right)i$ ship speed - $\frac{{d^2 }}{{dt^2 }}r_0 \left( t \right) = - \frac{{d^2 }}{{dt^2 }}x_0 \left( t \right)i$ ship acceleration - s unstretched distance along the cable - T t effective tension - T _i(s, t) axial tension in cable elementi - T _{n, 0} = –L _nH( theta

_n) axial tension in the beginning of elementn - T _ship(t) cable top force - 0054xx_{s, t} ldquo

true

axial force - t, n, b tangent, normal and binormal unit vectors - V _p ⁰ cable pay out rate - V ₀ initial ship speed - V _t,V _n,V _b tangential, normal and binormal components of cable element velocity vector - V _c(s, t),A _c(s, t) velocity and acceleration vectors of a cable element - w cable weight in sea water per unit length - w j self weight - X(s, t), Y(s, t) Z(s, t) functions describing cable geometric configuration - beta