A Note on the Computation of Maximum Roll Amplitudes in Regular Beam Seas

Generalized methods for deriving the harmonic balance equations are illustrated using a ship roll model with angle dependent cubic damping, and cubic stiffness terms. The balance equations are then solved subject to a phase constraint which identifies the resonant solution only. The amplitude of the response at resonance, and the frequency at which resonance occurs, can therefore be obtained without needing to compute the response over a wide frequency range. This provides an efficient tool for investigating the dependence of the resonant response on the level of input excitation, with results which agree well with more time-consuming simulation methods.

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Generalized Harmonic Analysis of Nonlinear Ship Roll Dynamics

Journal of Ship Research ◽

10.5957/jsr.1996.40.4.316 ◽

1996 ◽

Vol 40 (04) ◽

pp. 316-325

Author(s):

J. C. Peyton Jones ◽

I. Cankaya

Keyword(s):

Harmonic Analysis ◽

Harmonic Balance ◽

Initial Conditions ◽

Balance Equations ◽

Validation Process ◽

Algebraic Expressions ◽

Resonant Modes ◽

Ship Roll ◽

Righting Moment ◽

Simulation Time

Algebraic expressions are presented which enable the harmonic balance equations to be written down directly in terms of the coefficients of a general nonlinear ship roll equation, without restriction on the number of harmonics considered. The rolling response is then readily computed, as illustrated by an investigation of the resonant modes of ships with angle-dependent cubic damping, or quintic terms in the righting moment. Details are also given of the validation process, showing how simulation time can be reduced by an appropriate choice of initial conditions.

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Experimental Data on the Systematic Variation of the Internal Damping Inside a U-Shaped Anti-Roll Tank

Volume 7: Ocean Space Utilization; Professor Emeritus J. Randolph Paulling Honoring Symposium on Ocean Technology ◽

10.1115/omae2014-23799 ◽

2014 ◽

Cited By ~ 1

Author(s):

Michiel Gunsing ◽

Nicolas Carette ◽

Geert Kapsenberg

Keyword(s):

Roll Motion ◽

Internal Damping ◽

Frequency Range ◽

At Resonance ◽

Series Of Experiments ◽

Ship Roll ◽

Rotating Table ◽

Set Up ◽

Individual Design ◽

Ship Roll Motion

Anti-Roll Tanks (ARTs) can be a successful device to reduce ship roll motion (Figure 1), but the tank has to be properly designed. A good design includes an appropriate number of damping devices in the tank to reduce the water motions at resonance and to increase the frequency range over which the tank works efficiently. It is difficult to accurately predict the effect of different damping devices on the roll damping moment of the tank; usually tests on a rotating table, so called bench tests, are performed for each individual design. Nowadays, CFD (see e.g. [1]) calculations solving the URANS equations can predict the effect of damping devices on the roll motion of the tank. In order to validate such codes a series of experiments with a U-type ART on a rotating table have been carried out where the interior arrangement in the duct of the tank has been varied. The set-up of the experiment, the measurement system and the results of the experiments are presented and discussed in this publication; the raw data of the experiments are also made available.

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THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

CAD/EDA, MODELING AND SIMULATION IN MODERN ELECTRONICS: COLLECTION OF SCIENTIFIC PAPERS OF THE III INTERNATIONAL SCIENTIFIC AND PRACTICAL CONFERENCE ◽

10.30987/conferencearticle_5e0282123a4fa0.04742815 ◽

2019 ◽

Author(s):

Vladimir Lantsov ◽

A. Papulina

Keyword(s):

Harmonic Balance ◽

Model Order Reduction ◽

Order Reduction ◽

Balance Equations ◽

Model Order ◽

Cad Systems ◽

Computational Costs ◽

Reduction Methods ◽

Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

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