DYNAMIC INSTABILITY OF FLOATING BODIES IN REGULAR WAVES

Abstract

The asymptotic instability conditions of a two-dimensional rectangular floating body under regular longitudinal waves are studied. Various hydrodynamic forces exerted on the floating body , including Froude-Krylov force, damping force and added mass force, and their suitable formulations are investigated. Frequency-dependent added mass and damping ratio are adopted in the heave equation. For roll motion, a model with the cubic + quadratic angle dependent damping and constant added-mass-moment-of-inertia is used. It is pointed out in this work that the relative heave motion used for evaluating the added mass and damping forces should be based on the fluid kinematics at the instantaneous position of the bottom of the floating body; this can have a significant effect on the computed responses. A pressure distribution, which satisfies the boundary condition at the actual free surface, is obtained and used to derive the Froude-Krylov forces. It is shown that the heave responses obtained from the suggested model are more reasonable than those predicted by the commonly used heave model of linear oscillator, especially when the system is near the heave resonance. The roll instability conditions are obtained numerically and compared with the analytically derived results using the harmonic balance method. Several factors which can affect the instability conditions are also investigated.