# Analysis of Real Ship Rolling Dynamics under Wave Excitement Force Composed of Sums of Cosine Functions

## Abstract

The ship motion equation with a cosine wave excitement force describes the slip moments in regular waves. A new kind of wave excitement force model, with the form as sums of cosine functions was proposed to describe ship rolling in irregular waves. Ship rolling time series were obtained by solving the ship motion equation with the fourth-order-Runger-Kutta method. These rolling time series were synthetically analyzed with methods of phase-space track, power spectrum, primary component analysis, and the largest Lyapunove exponent. Simulation results show that ship rolling presents some chaotic characteristic when the wave excitement force was applied by sums of cosine functions. The result well explains the course of ship rolling's chaotic mechanism and is useful for ship hydrodynamic study.

- Authors:

- Department of Scientific Research, Dalian Naval Academy, Dalian 116018 (China)
- Department of Navigation, Dalian Naval Academy, Dalian 116018 (China)
- Department of Hydrography and Cartography, Dalian Naval Academy, Dalian 116018 (China)

- Publication Date:

- OSTI Identifier:
- 21611722

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1376; Journal Issue: 1; Conference: 6. international conference on fluid mechanics, Guangzhou (China), 30 Jun - 3 Jul 2011; Other Information: DOI: 10.1063/1.3651896; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; COMPUTERIZED SIMULATION; DIFFERENTIAL EQUATIONS; FREQUENCY MEASUREMENT; PHASE SPACE; ROLLING; RUNGE-KUTTA METHOD; SHIPS; SLIP; STOCHASTIC PROCESSES; CALCULATION METHODS; EQUATIONS; FABRICATION; ITERATIVE METHODS; MATERIALS WORKING; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; MATHEMATICS; NUMERICAL SOLUTION; SIMULATION; SPACE

### Citation Formats

```
Zhang, Y. S., Cai, F., and Xu, W. M.
```*Analysis of Real Ship Rolling Dynamics under Wave Excitement Force Composed of Sums of Cosine Functions*. United States: N. p., 2011.
Web. doi:10.1063/1.3651896.

```
Zhang, Y. S., Cai, F., & Xu, W. M.
```*Analysis of Real Ship Rolling Dynamics under Wave Excitement Force Composed of Sums of Cosine Functions*. United States. doi:10.1063/1.3651896.

```
Zhang, Y. S., Cai, F., and Xu, W. M. Wed .
"Analysis of Real Ship Rolling Dynamics under Wave Excitement Force Composed of Sums of Cosine Functions". United States. doi:10.1063/1.3651896.
```

```
@article{osti_21611722,
```

title = {Analysis of Real Ship Rolling Dynamics under Wave Excitement Force Composed of Sums of Cosine Functions},

author = {Zhang, Y. S. and Cai, F. and Xu, W. M.},

abstractNote = {The ship motion equation with a cosine wave excitement force describes the slip moments in regular waves. A new kind of wave excitement force model, with the form as sums of cosine functions was proposed to describe ship rolling in irregular waves. Ship rolling time series were obtained by solving the ship motion equation with the fourth-order-Runger-Kutta method. These rolling time series were synthetically analyzed with methods of phase-space track, power spectrum, primary component analysis, and the largest Lyapunove exponent. Simulation results show that ship rolling presents some chaotic characteristic when the wave excitement force was applied by sums of cosine functions. The result well explains the course of ship rolling's chaotic mechanism and is useful for ship hydrodynamic study.},

doi = {10.1063/1.3651896},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1376,

place = {United States},

year = {2011},

month = {9}

}