Validation of Volterra Series Approach for Modelling Parametric Rolling of Ships

2015 ◽  
Author(s):  
Abhilash S. Somayajula ◽  
Jeffrey M. Falzarano
Keyword(s):  
Validation Studies ◽  
Volterra Series ◽  
Equations Of Motion ◽  
Series Representation ◽  
Analytical Techniques ◽  
Simplified Model ◽  
Stability Criteria ◽  
Parametric Roll ◽  
Parametric Rolling ◽  
Following 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. 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.

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

2014 ◽  
Author(s):  
Abhilash S. Somayajula ◽  
Jeffrey M. Falzarano
Keyword(s):  
Volterra Series ◽  
Nonlinear Modeling ◽  
Series Representation ◽  
Nonlinear Damping ◽  
Regular Waves ◽  
Parametric Roll ◽  
Linear Dynamics ◽  
Following Seas ◽  
Ergodic Behavior ◽  
Non Linear

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.

Application of Volterra Series Analysis for Parametric Rolling in Irregular Seas

2014 ◽  
Vol 58 (02) ◽  
pp. 97-105
Author(s):  
Hisham Moideen ◽  
Abhilash Somayajula ◽  
Jeffrey M. Falzarano
Keyword(s):  
Volterra Series ◽  
Irregular Waves ◽  
Parametric Roll ◽  
Peak Period ◽  
Parametric Rolling ◽  
Motion Sensitivity ◽  
Direct Excitation ◽  
Head Waves ◽  
Metacentric Height ◽  
Regular Head Waves

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.

Investigation of the 2nd Generation of Intact Stability Criteria for Ships Vulnerable to Parametric Rolling in Following Seas

2013 ◽  
Author(s):  
Stefan Krüger ◽  
Hannes Hatecke ◽  
Heike Billerbeck ◽  
Anna Bruns ◽  
Florian Kluwe
Keyword(s):  
Dynamic Stability ◽  
Direct Calculation ◽  
Stability Criteria ◽  
Parametric Rolling ◽  
Following Seas ◽  
2Nd Generation ◽  
Direct Assessment ◽  
Intact Stability ◽  
New Criteria ◽  
Level 2

The existing IMO intact stability criteria (IS-Code 2008) do not generally provide sufficient safety against dynamic stability failures such as parametric rolling for modern ships. Therefore, new stability criteria have been developed by IMO / SLF. These so-called Second Generation Stability Criteria shall ensure sufficient dynamic stability. The criteria are structured in a three level approach, where the first level consists of quite simple formulae. If a ship does not pass the first level, it is assumed that the ship is vulnerable to the phenomenon addressed, and the second level of criteria shall then be applied. This level consists of computations which are a little more complex, but they still treat the problems addressed in a strongly simplified manner. If now the ship does not pass the second level, a third level shall be applied to ensure that the ship can be designed and operated safely. This third level consists of direct calculation methods which shall be applied, however no criteria or procedures have yet been developed for this third level. We have applied the level 1 and level 2 criteria to a reference ship where a direct stability assessment has been performed during the design. The results showed extremely large scatter in the required GM-values of the criteria, and none of the criteria showed GM values roughly comparable to the direct assessment. The paper shows why the application of the criteria is challenging for the design of RoRo-ships and why a third level (direct assessment) is urgently required before the first two levels are put into force. Some conclusions are also drawn for the possible treatment of the new criteria in a stability booklet.

Parametric Rolling Simulations of Container Ships

2013 ◽  
Author(s):  
Anton Turk ◽  
Jasna Prpić-Oršić ◽  
Carlos Guedes Soares
Keyword(s):  
Time Domain ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Full Range ◽  
Ship Motions ◽  
Computationally Efficient ◽  
Parametric Roll ◽  
Parametric Rolling ◽  
Strip Theory ◽  
The Time Domain

A hybrid nonlinear time domain seakeeping analysis is applied to the study of a container ship advancing at different headings and encounter frequencies. A time-domain nonlinear strip theory in six degrees-of-freedom has been extended to predict ship motions by solving the unsteady hydrodynamic problem in the frequency domain and the equations of motion in the time domain which allows introducing nonlinearities in the linear model. The code is used to make parametric roll predictions for various speeds and headings and the results are summarized in a very intuitive 2D and 3D polar plots showing the full range of the parametric rolling realizations. The method developed is fairly accurate, robust, very computationally efficient, and can predict nonlinear ship motions. It is well suited to be used as a tool in ship design or as part of a path optimization model.

Nonlinear Analysis of a Rigid Rotor on Magnetic Bearings

1995 ◽  
Author(s):  
C. Nataraj
Keyword(s):  
Nonlinear Analysis ◽  
Equations Of Motion ◽  
Forced Response ◽  
Magnetic Bearings ◽  
Rigid Rotor ◽  
Stability Criteria ◽  
Safe Operation ◽  
Qualitative And Quantitative ◽  
Quantitative Results ◽  
Nonlinear Equations Of Motion

A simple model of a rigid rotor supported on magnetic bearings is considered. A proportional control architecture is assumed, the nonlinear equations of motion are derived and some essential nondimensional parameters are identified. The free and forced response of the system is analyzed using techniques of nonlinear analysis. Both qualitative and quantitative results are obtained and stability criteria are derived for safe operation of the system.

Instantaneous Identification of Polynomial Nonlinearity Based on Volterra Series Representation

2005 ◽  
Vol 293-294 ◽  
pp. 703-710 ◽  
Author(s):  
Giacomo V. Demarie ◽  
Rosario Ceravolo ◽  
Alessandro de Stefano
Keyword(s):  
Structural Engineering ◽  
Volterra Series ◽  
Series Representation ◽  
Consistent Estimate ◽  
Short Time Fourier Transform ◽  
Dynamic Identification ◽  
Polynomial Nonlinearity ◽  
Definition Of ◽  
Short Time

In structural engineering applications a sufficient quantity of experimental data to be able to achieve a consistent estimate of nonlinear quantities is seldom available: this applies in particular when the structures are to be tested in situ. This report discusses the definition of instantaneous estimators to be used in the dynamic identification of invariant nonlinear systems on the basis of Short-Time Fourier Transform representation of excitation and system’s response and within the framework of a Volterra series representation of the input/output relationship. An estimation of the parameters of a dynamic system can be worked out from the evolution of such instantaneous estimators.

K-L Expansion of a Random Process in Wavelet Bases

1998 ◽  
Author(s):  
Om P. Agrawal ◽  
Shantaram S. Pai
Keyword(s):  
Eigenvalue Problem ◽  
Wavelet Transforms ◽  
Series Representation ◽  
Numerical Algorithms ◽  
Analytical Techniques ◽  
Random Processes ◽  
Random Coefficients ◽  
Engineering Systems ◽  
Wavelet Bases ◽  
Orthogonal Wavelets

Abstract Random processes play a significant role in stochastic analysis of mechanical systems, structures, fluid mechanics, and other engineering systems. In this paper, a numerical method for series representation of random processes, with specified mean and correlation functions, in wavelet bases is presented. In this method, the Karhunen-Loeve expansion approach is used to represent a process as a linear sum of orthonormal eigenfunctions with uncorrelated random coefficients. The correlation and the eigenfunctions are approximated as truncated linear sums of compactly supported orthogonal wavelets. The eigenfunctions satisfy an integral eigenvalue problem. Using the above approximations, the integral eigenvalue problem is converted to a matrix (finite dimensional) eigenvalue problem. Numerical algorithms are discussed to compute one- and two-dimensional wavelet transforms of certain functions, and the resulting equations are solved to obtain the eigenvalues and the eigenfunctions. The scheme provides an improvement over other existing schemes. Two examples are considered to show the feasibility and effectiveness of this method. Numerical studies show that the results obtained using this method compare well with analytical techniques.

scholarly journals Long-Term Predictions for Highly Eccentric Orbits

1993 ◽  
Vol 132 ◽  
pp. 353-363
Author(s):  
José M. Ferrándiz ◽  
M. Eugenia Sansaturio ◽  
Jesús Vigo
Keyword(s):  
Equations Of Motion ◽  
Analytical Techniques ◽  
Artificial Satellites ◽  
Numerical Techniques ◽  
Dynamical Models ◽  
Eccentric Orbits

AbstractPredictability in orbital behaviour of artificial satellites depends on several factors: the accuracy required, the particular dynamical models formulated, the sets of variables chosen to describe them, the numerical or analytical techniques used and, specially, the specific trajectories to be established. In this paper we address the problem of predictability for highly eccentric satellites with (J2 + J22)-perturbation, by using numerical techniques to integrate the equations of motion when expressed in different sets of regular variables.

Experimental Analysis of a Planar Reconfigurable Mechanism With a Variable Joint

2016 ◽  
Author(s):  
Peter W. Malak ◽  
Anthony J. Buchta ◽  
Philip A. Voglewede
Keyword(s):  
Optimal Control ◽  
Transition Point ◽  
Physical Mechanism ◽  
Equations Of Motion ◽  
Angular Position ◽  
The Other ◽  
Simplified Model ◽  
Physical Prototype ◽  
Kinetics Of ◽  
Kinematics And Kinetics

Previously a specific planar reconfigurable mechanism with a variable joint (RRRR1 -RRRP2 Mechanism) was dynamically modeled. The RRRR-RRRP Mechanism functions as a RRRR mechanism in one configuration and as a in RRRP mechanism the other. The kinematics and kinetics of the RRRP and RRRR configurations were previously analyzed with a Lagrangian approach. The developed equations of motion will be validated with a physical prototype in this paper. In addition, a simplified model of the RRRR-RRRP Mechanism is also developed and compared to the experimental results. The experimental angular position of each joint on the RRRR-RRRP Mechanism will be compared to the model position analysis. Particular attention will be given to the transition point when the physical mechanism changes from an RRRR mechanism to RRRP mechanism and vice versa as it is vital to knowing this point for optimal control of the mechanism.

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