Abhilash Somayajula

Non-Linear Dynamics of Parametric Roll of Container Ship in Irregular Seas

Parametric motion is the phenomenon where a structure is excited into large amplitude motion even when there is no direct excitation. A well-known example of this type of motion is the parametric roll of ships in head or following seas. Parametric roll of container ships in head seas is relatively a new problem which has gained much importance after the catastrophic incidence of APL China in 1998. Many studies have investigated this phenomenon in the case of a ship being excited in regular waves. However, ships do not encounter regular waves in the actual ocean. So, it is imperative to study the importance of parametric roll in irregular seas.In this paper the analysis of roll equation of motion is performed by nonlinear modeling. The problem of parametric roll is approached as a non-linear dynamics problem with due consideration to nonlinear time varying hydrostatics as well as the nonlinear damping. A nonlinear damping model is used to approximate the actual viscous damping in the system. The variation of the roll righting arm with time has been modeled using a Volterra series representation which includes the hydrostatic non-linearity.Various realizations of the roll motion have been simulated and analyzed to study the ergodic behavior of the phenomenon. The paper also discusses future ideas of how to analyze parametric roll in irregular seaways.Copyright

Application of Volterra Series Analysis for Parametric Rolling in Irregular Seas

Parametric roll is a phenomenon in which there is a large rolling motion of a ship even when the ship is moving into head seas with no direct excitation. It is a nonlinear dynamic phenomenon of a ship rolling system with nonlinearities in the stiffness as well as the damping terms. Parametric roll of container ships in head seas is a relatively new problem, which has gained lot of importance after the catastrophic incidence of APL China in 1998. Analysis of parametric roll of container ships in regular head waves has been studied extensively. However, the ships do not encounter regular waves in the ocean. So, it is necessary to study how important parametric roll is in irregular seas. To study this, it is first important to model the variation of metacentric height in irregular waves, which is nonlinear as a result of the influence of underwater geometry and the motions of the ship in a seaway. In this work, the change of metacentric height (GM) in irregular waves has been modeled using a Volterra series approach. This transfer function for metacentric height (GM) is used to study parametric rolling of ships in irregular waves. Based on this study, roll motion sensitivity to the spectral peak period and significant wave height has been carried out.

Parametric Roll of High Speed Ships in Regular Waves

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.Copyright

Validation of Volterra Series Approach for Modelling Parametric Rolling of Ships

Parametric motion is the phenomenon where a structure is excited into large amplitude motion even when there is no direct excitation. A well-known example of this type of motion is the parametric roll of ships in head or following seas. Parametric roll of container ships in head seas is relatively a new problem which has gained much importance after the catastrophic incidence of APL China in 1998. Although a lot of analytical techniques are available on the assessment of parametric roll in regular excitation, not many investigations have explored its occurrence in irregular seas. A consensus on the stability criteria to assess the danger due to this phenomenon in actual ocean has not yet been reached making it an active area of investigation.A precursor to the development of stability criteria is a simple model to capture the phenomenon of parametric rolling. However, it is important that the model is not over simplified and ignores important dynamics of the process. Therefore it is necessary to perform validation studies between the simplified model and the complete nonlinear model capturing all the physics of the phenomenon.This paper provides the validation studies of a 1-DOF (degree of freedom) simplified model for roll motion against a standard 6-DOF time domain simulation approach. The 1-DOF model is based on the Volterra series representation of the hydrostatic stiffness in waves while accounting for the heave and pitch motions of the model. It also includes a nonlinear damping model capturing the radiation and the viscous damping. The 6-DOF model solves for the nonlinear equations of motion based on Euler angles and also includes the nonlinear Froude Krylov excitations and nonlinear hydrostatic forces on the vessel. Details of the modeling in the two approaches are described and comparisons are performed to assess the validity of 1-DOF simplified model.Copyright

A Comparative Assessment of Simplified Models for Simulating Parametric Roll

The motion of a ship/offshore platform at sea is governed by a coupled set of nonlinear differential equations. In general, analytical solutions for such systems do not exist and recourse is taken to time-domain simulations to obtain numerical solutions. Each simulation is not only time consuming but also captures only a single realization of the many possible responses. In a design spiral when the concept design of a ship/platform is being iteratively changed, simulating multiple realizations for each interim design is impractical. An analytical approach is preferable as it provides the answer almost instantaneously and does not suffer from the drawback of requiring multiple realizations for statistical confidence. Analytical solutions only exist for simple systems, and hence, there is a need to simplify the nonlinear coupled differential equations into a simplified one degree-of-freedom (DOF) system. While simplified methods make the problem tenable, it is important to check that the system still reflects the dynamics of the complicated system. This paper systematically describes two of the popular simplified parametric roll models in the literature: Volterra GM and improved Grim effective wave (IGEW) roll models. A correction to the existing Volterra GM model described in current literature is proposed to more accurately capture the restoring forces. The simulated roll motion from each model is compared against a corresponding simulation from a nonlinear coupled time-domain simulation tool to check its veracity. Finally, the extent to which each of the models captures the nonlinear phenomenon accurately is discussed in detail. [DOI: 10.1115/1.4034921]

Volterra approach – a new method to accurately calculate the non-linear and time-varying roll restoring arm of ships in irregular longitudinal seas

ABSTRACT With several incidents of large amplitude roll motion of ships observed at sea over the past two decades, the dynamic stability of modern ship types has assumed significant importance. The move by the International Maritime Organization to develop a second generation level-2 criteria has resulted in considerable attention to the development of simplified analytical models for roll motion. Especially for the problem of parametric roll, there is still no analytical model which accurately captures the non-linear roll restoring stiffness taking into account the combined effect of incident waves and dynamic heave and pitch motions of the vessel. This paper extends our previous work to accurately capture both the linear and higher-order time-varying roll stiffness coefficients through an analytical model while taking into account incident waves and dynamic motion of the vessel. This approach called the Volterra method is compared against the existing simplified models and a non-linear time-domain simulation program to demonstrate better agreement of the proposed approach.