Nonlinear Springing of a Ship in Irregular Head Seas.

Abstract

Fluid forces which excite a vertical two-node flexural vibration of a ship in forward motion in irregular head seas are considered in this work. Nonlinear "sum frequency" flow interactions, which often induce a vibration at the ship's resonant response frequency, are investigated through analytical and experimental studies. The flow problem is theoretically formulated in the context of ideal fluid theory, and the analysis is conducted through use of a perturbation expansion in a small "wave slope" parameter. Nonlinear effects are included by retaining terms which are of second order in this small quantity. Approximations are introduced to simplify the analysis through exploitation of the geometric characteristics of the ship's form ("slenderness"), and the flexural rigidity of the hull's internal structure. The results of extensive model test experiments conducted by Slocum and Troesch (1983) are presented and discussed. The experiments include investigations of the sensitivity of the nonlinear component of the flexural vibration to wave frequency, wave amplitude, ship speed, structural stiffness, and motions in the heave and pitch modes. Numerical computations, based upon the analytical work, are presented and compared to the model test results. Reasonable agreement is obtained.