Parametric Roll of High Speed Ships in Regular Waves

Abstract

Analysis of ship parametric roll has generally been restricted to simple analytical models and sophisticated time domain simulations. Simple analytical models do not capture all the critical dynamics while time-domain simulations are often time consuming to implement. The model presented in this paper captures the essential dynamics of the system without over simplification. This work incorporates various important aspects of the system and assesses the significance of including or ignoring these aspects. Special consideration is given to the fact that a hull form asymmetric about the design waterline would not lead to a perfectly harmonic variation in metacentric height. Many of the previous works on parametric roll make the assumption of linearized and harmonic behavior of the time-varying restoring arm or metacentric height. This assumption enables modeling the roll motion as a Mathieu equation. This paper provides a critical assessment of this assumption and suggests modeling the roll motion as a Hills equation. Also the effects of non-linear damping are included to evaluate its effect on the bounded parametric roll amplitude in a simplified manner.

Added resistance and parametric roll prediction as a design criteria for energy efficient ships

“…In order to perform a time domain simulation, it is necessary to correctly estimate the variation of linear stiffness γ(τ) in irregular waves. In this section, the variation in GM with time shall be derived as a Volterra series based on the works of Hua et al (1999) and Moideen (2010) (Moideen et al 2013).…”

Large-amplitude time-domain simulation tool for marine and offshore motion prediction

“…Spyrou [41] has suggested the development of probabilistic framework to come up with analytical criteria for parametric roll in following seas. Moideen et al [24] developed 3D stability charts by including the nonlinear damping as a function of roll amplitude for regular wave analysis [25]. Umeda et al [44] performed time-domain simulations with calculating the Froude-Krylov forces up to the instantaneous incident waterline and diffraction forces using the instantaneous body position (calculated by strip theory method developed by Salvesen et al [36]) at each time step and compared them against experimentally measured time series.…”

An overview of the prediction methods for roll damping of ships

“…In addition to the effect on roll dynamic magnification (Response Amplitude Operator -RAO), the damping is also important in a variety of phenomena associated with roll motions such as broaching, surf-riding, parametric rolling (Moideen et al 2014(Moideen et al , 2013(Moideen et al , 2012 etc. In the analysis of Corresponding author, Ph.D. Student, E-mail: sabhilash@email.tamu.edu a Professor, E-mail: jfalzarano@civil.tamu.edu many unstable phenomena such as parametric rolling (Somayajula and Falzarano 2015b or capsizing in beam seas Falzarano 2013, 2011), the damping determines the stability criteria to avoid catastrophic failure.…”