Forces and Moments on a Small Body Moving in a 3-D Unsteady Flow (With Applications to Slender Structures)

[+] Author and Article Information
L. Foulhoux

Production, Elf Aquitaine, Marine Advanced Techniques Section, Pau, France

M. M. Bernitsas

Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109-2145

J. Offshore Mech. Arct. Eng 115(2), 91-104 (May 01, 1993) (14 pages) doi:10.1115/1.2920105 History: Received October 06, 1991; Revised October 15, 1992; Online June 12, 2008


Complete expressions are derived for the inertia forces and moments acting on a small body in a six-degree-of-freedom motion in a three-dimensional unsteady flow in an unbounded ideal fluid. The far-field approximation of the body motion is represented by a series of multipoles located at the origin of the body. Unsteady terms are expanded in a dual series to the multipole series. Lagally integrals are expressed in terms of multipoles as well, by using Legendre polynomial expansions. New inertia force expressions are derived by truncating the multipole series after the quadrupoles. Corresponding terms for moments are also developed. The derived formulas are still compact enough for engineering applications. Many practical problems involving fixed and oscillating cylinders, piles, and risers are studied numerically. Comparisons to the Morison equation formulation prove that the nonlinear convective terms are not negligible in multidimensional relative flows.

Copyright © 1993 by The American Society of Mechanical Engineers
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