Jeffrey M. Falzarano

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.

Estimation of hydrodynamic forces and motion of ships with steady forward speed

The growing number of large ships demands predicting their optimum performance with respect to travel time, fuel efficiency and the safety of cargo and personnel in specified shipping routes. This can be achieved using efficient and easy to use numerical tools capable of predicting hydrodynamic loads on floating vessels with steady forward speed and solving their motion response in various wave conditions. A three-dimensional potential theory based code using the Green function method is developed with consideration of forward speed effects. The generalized coordinate system is used to allow motion response calculations with respect to any desired body coordinate system and a common quadrilateral meshing format. The formulation and calculation of added mass and damping coefficients at zero and infinite frequency in forward speed case has been also provided. A number of structures including simple geometries and full ship hull forms have been analyzed and validated against published theoretical, numerical and experimental results. The comparison results are found to be in excellent agreement. The theoretical formulation, numerical implementation and result comparisons are presented here.

Development of a Computer Program for Three Dimensional Analysis of Zero Speed First Order Wave Body Interaction in Frequency Domain

Evaluation of motion characteristics of ships and offshore structures at the early stage of design as well as during operation at the site is very important. Strip theory based programs and 3D panel method based programs are the most popular tools used in industry for vessel motion analysis. These programs use different variations of the Green’s function or Rankine sources to formulate the boundary element problem which solves the water wave radiation and diffraction problem in the frequency domain or the time domain.This study presents the development of a 3D frequency domain Green’s function method in infinite water depth for predicting hydrodynamic coefficients, wave induced forces and motions. The complete theory and its numerical implementation are discussed in detail. An in house application has been developed to verify the numerical implementation and facilitate further development of the program towards higher order methods, inclusion of forward speed effects, finite depth Green function, hydro elasticity, etc. The results were successfully compared and validated with analytical results where available and the industry standard computer program for simple structures such as floating hemisphere, cylinder and box barge as well as complex structures such as ship, spar and a tension leg platform.© 2013 ASME

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

Combined Steady State and Transient Analysis of a Patrol Vessel as Affected by Varying Amounts of Damping and Periodic and Random Wave Excitation

In this paper various techniques of dynamical system analysts are used to analyze the effect of damping on large amplitude nonlinear ship-rolling motion of a patrol vessel. In particular steady state magnification curves, Poincare maps are for harmonic forcing and project phase planes are for random forcing. It has been found that varying amounts of damping substantially affect the vessels critical behavior. This is important since most stability regulations ignore damping and solely concentrate on the vessels righting ram curve. Moreover roll damping is difficult to predict accurately and small changes in damping may have a significant effect.

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]

Effect of Icing on Ship Maneuvering Characteristics

In this paper the effect of icing forward on the maneuvering characteristics of a small offshore supply vessel hull form, which was used for acoustic surveys in the North Atlantic by the US Navy during the Cold War, is studied. Icing is well known to compromise the roll motion stability of vessels but its effect on maneuvering and specifically path stability is not as well known. Using available empirical formulas for maneuvering coefficients and steady turning ability the effect of icing on the path stability and steady turning ability of this vessel are approximately evaluated. The results show that icing does affect the maneuverability but more study is required to more precisely quantify this effect.Copyright

Effect of More Accurate Hydrodynamic Modeling on Calculating Critical Nonlinear Ship Rolling Response

It is well known in the marine hydrodynamics field that the radiated wave force is frequency dependent. However, much work in the nonlinear marine dynamical systems field has assumed frequency independence or a constant coefficients approximation. Assuming constant coefficients may be a reasonable approximation for single frequency steady state motion and even the transient response of a nonlinear system with a single frequency excitation but clearly not for multiple frequency excitation. In this work we will assess the effect of approximating the radiated wave force by constant coefficients versus the more accurate impulse response function modeling. We will apply these two types of hydrodynamic force modeling to calculate critical dynamics of ship rolling motion in regular and irregular waves. The critical dynamics are directly determined using a unique calculation method (Vishnubhotla, Falzarano, Vakakis, 2000). This method directly calculates motions on either the stable and unstable manifolds. Since the stable manifolds form the basin boundaries, the safe basin can be defined. Moreover, this method can be used as an alternative to the so-called Melnikov method by directly calculating the distance between the stable and unstable manifolds. This method is potentially more powerful than Melnikov methods since is it not dependent upon the so-called “Melnikov trick” which practically limits the Melnikov method to first order. This paper will contain results of constant coefficients (for various constant frequencies) versus impulse response function for regular wave excitation and various spectra.