Complete Six-Degrees-of-Freedom Nonlinear Ship Rolling Motion

[+] Author and Article Information
M. Taz Ul Mulk, J. Falzarano

School of Naval Architecture and Marine Engineering, 911 Engineering Building, University of New Orleans, New Orleans, LA 70148

J. Offshore Mech. Arct. Eng 116(4), 191-201 (Nov 01, 1994) (11 pages) doi:10.1115/1.2920150 History: Received June 16, 1993; Revised June 14, 1994; Online June 12, 2008


The emphasis of this paper is on nonlinear ship roll motion, because roll is the most critical ship motion of all six modes of motion. However, coupling between roll and the other modes of motion may be important and substantially affect the roll. Therefore, the complete six-degrees-of-freedom Euler’s equations of motion are studied. In previous work (Falzarano et al., 1990, 1991), roll linearly coupled to sway and yaw was studied. Continuing in this direction, this work extends that analysis to consider the dynamically more exact six-degrees-of-freedom Euler’s equations of motion and associated Euler angle kinematics. A combination of numerical path-following techniques and numerical integrations are utilized to study the steady-state response determined using this more exact modeling. The hydrodynamic forces are: linear frequency-dependent added-mass, damping, and wave-exciting, which are varied on a frequency-by-frequency basis. The linearized GM approximation to the roll-restoring moment is replaced with the nonlinear roll-restoring moment curve GZ(φ), and the linear roll wave damping is supplemented by an empirically derived linear and nonlinear viscous damping. A particularly interesting aspect of this modeling is the asymmetric nonlinearity associated with the heave and pitch hydrostatics. This asymmetric nonlinearity results in distinctive “dynamic bias,” i.e., a nonzero mean in heave and pitch time histories for a zero mean periodic forcing, and a substantial second harmonic. A Fourier analysis of the nonlinear response indicates that the harmonic response is similar to the linear motion response.

Copyright © 1994 by The American Society of Mechanical Engineers
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