Arthur M. Reed

Probability of Capsizing in Beam Seas with Piecewise Linear Stochastic GZ Curve

The probability of capsizing for a dynamical system with time-varying piecewise linear stiffness is presented. The simplest case is considered, in which only the angle of the maximum of the restoring curve is changing. These changes are assumed to be dependent on wave excitation; such a system can be considered as a primitive model of a ship in beam seas, where all changes in stability are caused by heave motions. A split-time approach is used, in which capsizing is considered as a sequence of two random events: upcrossing through a certain threshold (non14 rare problem) and capsizing after upcrossing (rare problem). To reflect the time15 varying stability, a critical roll rate is introduced as a stochastic process defined at any instant of time. Capsizing is then associated with an upcrossing when the instantaneous roll rate exceeds the critical roll rate defined for the instant of upcrossing. A self-consistency check of the method, in which a statistical frequency of capsizing was obtained by time-domain evaluation of the response of the piecewise linear dynamical system and favorably compared with the theoretical prediction is described.

A Naval Perspective on Ship Stability

From a naval perspective, three areas have been identified as critical for examining the performance of vessels in extreme seas: the physics of large-amplitude motions; verification, validation and accreditation (VVA and performance-based criteria. In the physics of large-amplitude motions, three topics are most important: hydrodynamic forces, maneuvering in waves, and largeamplitude roll damping. In the VV&A arena, the challenge remains for performing this function for extreme seas conditions, where linear concepts such as response amplitude operators are not applicable. The challenge of performance-based criteria results from the fact that it is on the leading edge of our knowledge base.

A PIECEWISE MODEL FOR PREDICTION OF LARGE AMPLITUDE TOTAL SHIP ROLL DAMPING

A piecewise model is presented to model total ship roll damping, with considerations for large amplitude roll motion effects, such as bilge keel interaction with the free-surface. The model is based on the consideration of distinct ship-specific physical phenomena, such as bilge keel emergence. Abrupt physical changes occur with these events, resulting in significant changes in the damping characteristics of the system. Without these considerations, roll motion may be under-predicted. Some additional considerations needed for the practical implementation of the proposed piecewise model are also discussed.Copyright