Abstract
The responses (displacements, distortions, bending moments, etc.) of a structure departing from uniform motion in a fluid, are modelled by a system of N nonlinear second order ordinary differential equations. In seeking a solution, this system is transformed into a system of 2N first order nonlinear equations and numerical methods for obtaining the solution are derived by making approximations to the exponential function in a recurrence relation. Special attention is given to methods for solving problems for which the solution (i) decays monotonically, (ii) oscillates and decays, (iii) oscillates without growth, and (iv) oscillates and grows. The numerical methods are analysed, used in predictor-corrector combination, and globally extrapolated to improve accuracy. Numerical results obtained are seen to compare favourably with published results relating to a semi-submersible in waves.
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