# Investigation of a Cabin Suspended and Articulated Rescue Vessel in Terms of Motion Reduction

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structure of the Rescue Vessel

#### 2.1. Overall Structure of Rescue Vessel

#### 2.2. Design Characteristics of the Rescue Vessel

#### 2.2.1. Suspension System

#### 2.2.2. Multi-Degree-of-Freedom Articulated System

#### 2.3. Kinematic Description of the System

_{1}and k

_{2}are the equivalent stiffness coefficients of the flexible pontoon and suspension system. μ is the equivalent damping coefficient of the suspension system. w

_{l}and w

_{r}are the displacement excitations of the waves for the left and right pontoons in the vertical direction, respectively, z

_{1l}and z

_{1r}are the displacements of the left and right pontoons in the vertical direction, respectively, z

_{2}is the displacement in the vertical direction of the center of mass of the rescue platform, and θ is the roll angle of the rescue platform.

## 3. Modeling and Experimental Verification of Rescue Vessel

#### 3.1. Whole Vessel Dynamics Model Based on SimMechanics

#### 3.2. Experimental Verification

#### 3.2.1. Experiment on Water

#### 3.2.2. Data Pre-Processing

#### 3.2.3. Model Validation

## 4. Study of Key Parameters

^{−1}and the damping ratio is 0.6; that is, the damping coefficient of a single suspension system is 294 Ns·m

^{−1}. During voyages and operations at sea, vessels usually encounter beam waves, head waves, bow waves, and large heave motion [37], among which bow waves can be regarded as the combination of head waves and beam waves. Hence, the SimMechanics model is used to simulate the rescue vessel during bow waves and large heave motion, and the dynamic characteristics of the suspension system are analyzed. The input frequency of wave impact is 0.8 Hz, and the amplitude refers to the displacements of the experimental data at the pontoon, which are 0.1 m, 0.25 m, and 0.4 m. The input method and the animation are shown in Figure 11.

#### 4.1. Simulation with Large Heave Motion

^{−1}, the root mean square value of the acceleration at the mass center of the rescue platform is the minimum, and the dynamic stroke of the suspension system does not exceed the maximum stroke, so the damping value of 221 Ns·m

^{−1}is used as the reference value for the following stiffness coefficient study.

^{−1}and the damping coefficient is 221 Ns·m

^{−1}, the damping ratio is 0.45. For this study, the damping values are adjusted for each simulation to keep the damping ratios constant using Equation (2) for the damping ratio [38].

#### 4.2. Simulation with Bow Waves

#### 4.3. Conclusions from the Study of Key Parameters

^{−1}and 9000 N·m

^{−1}, and the damping coefficients are 190 Ns·m

^{−1}and 622 Ns·m

^{−1}. From the overall trend, the working condition with a large heave motion has little effect on the safety of the suspension system, and the stiffness coefficient and the damping coefficient are smaller, which is more helpful for the effect of buffering and absorbing vertical movement. However, under the working condition of bow waves, this causes a larger amplitude of the suspension system’s dynamic stroke, so it requires a larger stiffness and damping coefficient of the suspension system to support the rescue platform and buffer the vertical movement. Specifically, under the condition of bow waves, it is necessary to increase 100% of the reference stiffness coefficient to ensure that the limited block is not touched with the impact of the large amplitude. When selecting the parameters of the actual suspension system in the prototype vessel, it is necessary to refer to this ultimate working condition for the calibration of the parameters.

## 5. Discussion

#### 5.1. Effect of the Suspension System on Seakeeping

#### 5.2. Effect of the Articulated System on Seakeeping

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Qianqian, L.; Wang, Q. A comparative study on uncooperative search models in survivor search and rescue. Nat. Hazards
**2017**, 89, 843–857. [Google Scholar] [CrossRef] - Ma, X.; Karimpour, A.; Wu, Y. Statistical evaluation of data requirement for ramp metering performance assessment. Transp. Res. Part A Policy Pract.
**2020**, 141, 248–261. [Google Scholar] [CrossRef] - Kolltveit, B. Book Review: Rescue at Sea: An International History of Lifesaving, Coastal Rescue Craft and Organisations. Int. J. Marit. Hist.
**2004**, 16, 263–264. [Google Scholar] [CrossRef] - Cain, C. Design for Safety: A Practical Approach and Its Implementation within the Royal National Lifeboat Institution. Ph.D. Thesis, University of Newcastle upon Tyne, Newcastle upon Tyne, UK, 2002. [Google Scholar]
- Chen, D. Brief Analysis on “Huaying”. How to Play the Role of Offshore Search and Rescue. Pearl River Water Transp.
**2013**, 2, 58–59. [Google Scholar] [CrossRef] - Jiang, Y.; Ding, Y.; Sun, Y.; Shao, Y.; Sun, L. Influence of bilge-keel configuration on ship roll damping and roll response in waves. Ocean. Eng.
**2020**, 216, 107539. [Google Scholar] [CrossRef] - Liu, X.; Zhao, W.W.; Wan, D. Optimization of the roll motion of box-shaped hull section with anti-rolling sloshing tanks and fins in beam waves. J. Hydrodyn.
**2021**, 33, 688–697. [Google Scholar] [CrossRef] - Ren, R.-Y.; Zou, Z.-J.; Wang, J.-Q. Time-Scale Decomposition Techniques Used in the Ship Path-Following Problem with Rudder Roll Stabilization Control. J. Mar. Sci. Eng.
**2021**, 9, 1024. [Google Scholar] [CrossRef] - Zhao, J.; Liang, C.; Zhang, X. Rudder Roll Stabilization Based on Arc Tangent Nonlinear Feedback for Ships. J. Mar. Sci. Eng.
**2020**, 8, 245. [Google Scholar] [CrossRef] [Green Version] - Subramanian, R.; Jyothish, P.V. Genetic Algorithm Based Design Optimization of a Passive Anti-Roll Tank in a Sea Going Vessel. Ocean. Eng.
**2020**, 203, 107216. [Google Scholar] [CrossRef] - Alujević, N.; Ćatipović, I.; Malenica, Š.; Senjanović, I.; Vladimir, N. Stability, performance and power flow of active U-tube anti-roll tank. Eng. Struct.
**2020**, 211, 110267. [Google Scholar] [CrossRef] - Hirakawa, Y.; Hirayama, T.; Kakizoe, K.; Takayama, T.; Funamizu, S.; Okada, N.; Yamane, A. Sea trial of prototype Vertical Weight Stabilizer (VWS) anti-rolling system for small ships. J. Mar. Sci. Technol.
**2014**, 19, 292–301. [Google Scholar] [CrossRef] - Yamada, M.; Higashiyama, H.; Namild, M.; Kazao, Y. Active vibration control system using a gyro-stabilizer. Control. Eng. Pract.
**1996**, 5, 1217–1222. [Google Scholar] [CrossRef] - Zhang, X.; Liu, Q.; Liu, J.; Zhu, Q.; Hu, H. Using gyro stabilizer for active anti-rollover control of articulated wheeled loader vehicles. Proc. Inst. Mech. Eng. Part I J. Syst. Control. Eng.
**2021**, 235, 237–248. [Google Scholar] [CrossRef] - Bahrami, H.; Ghassemi, H. Dynamic Motions of the Cabin Mounted on the Mono-Hull Planing Boat Using Suspension System in Waves. Pol. Marit. Res.
**2022**, 29, 13–25. [Google Scholar] [CrossRef] - Takahashi, T.; Arinaga, S.; Ishii, T. Investigation into the technical feasibility of a hi-stable cabin craft. Trans. West-Jpn. Soc. Naval Arch.
**1986**, 72, 213–226. [Google Scholar] - Kihara, K.; Hamada, C.; Ohnaka, S.; Kitamura, T. Development of a 200 passenger histable cabin craft, Trans. West-Jpn. Soc. Naval Arch.
**1991**, 81, 57–69. [Google Scholar] - Marine Advanced Robotics. Available online: https://wam-v.com/ (accessed on 5 November 2022).
- Mousaviraad, M.; Conger, M.; Stern, F. Validation of CFD-MBD FSI for High-Fidelity Simulations of Full-Scale WAM-V Sea-Trials with Suspended Payload. In Proceedings of the 13th International Conference on Fast Sea Transportation, Washington, DC, USA, 1 September 2015. [Google Scholar] [CrossRef]
- Mousaviraad, M.; Conger, M.; Bhushan, S.; Stern, F.; Peterson, A.; Ahmadian, M. Coupled computational fluid and multi-body dynamics suspension boat modeling. J. Vib. Control.
**2018**, 24, 4260–4281. [Google Scholar] [CrossRef] - Velodyne Marine. Available online: http://www.velodynemarine.com/ (accessed on 5 November 2022).
- Walker, L.; Longman, M.; Kawamata, A. Nauti-Craft Marine Suspension System—Suspension System to Reduce Vesselʼs Vibration and Improve Its Deck Attitude. Mar. Eng.
**2022**, 57, 227–234. [Google Scholar] [CrossRef] - Li, J.; Xiong, W.; Wang, H.T. The Research on Modeling and Simulation of Wave Adaptive Vessel. In Proceedings of the 2019 IEEE 8th International Conference on Fluid Power and Mechatronics (FPM), Wuhan, China, 10–13 April 2019; pp. 1055–1059. [Google Scholar] [CrossRef]
- Clauss, G.N.F.; Often, N.; Kauffeldt, A.; Otten, N.; Stuppe, S. Hull Optimization of the unmanned AGaPaS Rescue Vessel. In Proceedings of the ASME 29th International Conference on Ocean, Offshore and Arctic Engineering, Shanghai, China, 6–11 June 2010. [Google Scholar]
- Wang, Z.; Zhang, T.; Zhang, Z.; Yuan, Y.; Liu, Y. A high-efficiency regenerative shock absorber considering twin ball screws transmissions for application in range-extended electric vehicles. Energy Built Environ.
**2020**, 1, 36–49. [Google Scholar] [CrossRef] - Abid, H.J.; Chen, J.; Nassar, A.A. Equivalent Air Spring Suspension Model for Quarter-Passive Model of Passenger Vehicles. Int. Sch. Res. Not.
**2015**, 2015, 974020. [Google Scholar] [CrossRef] - Jiang, Z.-b.; Shao, L.; Shao, F. Numerical simulation of the spreading dynamic responses of the multibody system with a floating base. J. Mar. Sci. Appl.
**2015**, 14, 290–301. [Google Scholar] [CrossRef] - Dhanak, M.R.; Ananthakrishnan, P.; Frankenfield, J.; von Ellenrieder, K. Seakeeping Characteristics of a Wave-Adaptive Modular Unmanned Surface Vehicle. In Proceedings of the International Conference on Ocean, Offshore and Arctic Engineering, Nantes, France, 9–14 June 2013; p. V009T12A053. [Google Scholar]
- Zhai, Y.; Zhao, H.; Li, X.; Shi, W. Hydrodynamic Responses of a Barge-Type Floating Offshore Wind Turbine Integrated with an Aquaculture Cage. J. Mar. Sci. Eng.
**2022**, 10, 854. [Google Scholar] [CrossRef] - Hussain, S.; Jamwal, P.K.; Munir, M.T. Computer-Aided Teaching Using SimMechanics and Matlab for Project-Based Learning in a Robotics Course. Int. J. Soc. Robot.
**2022**, 14, 85–94. [Google Scholar] [CrossRef] - Gaber, A.N.A.E.; Eldrainy, Y.A.; Awad, T.H. Uncertainty solution of robot parameters using fuzzy position control applied for an automotive cracked exhaust system inspection. Alex. Eng. J.
**2021**, 60, 2355–2367. [Google Scholar] [CrossRef] - Hu, J.; Xiao, Q.; Li, R. Numerical Simulation of a Multi-Body System Mimicking Coupled Active and Passive Movements of Fish Swimming. J. Mar. Sci. Eng.
**2021**, 9, 334. [Google Scholar] [CrossRef] - Stošović, M.A.; Topisirović, D.; Litovski, V. Frequency and time domain comparison of selective polynomial filters with corrected phase characteristics. Int. J. Electron.
**2019**, 106, 770–784. [Google Scholar] [CrossRef] - Robertson, D.G.E.; Dowling, J.J. Design and responses of Butterworth and critically damped digital filters. J. Electromyogr. Kinesiol. Off. J. Int. Soc. Electrophysiol. Kinesiol.
**2003**, 13, 569–573. [Google Scholar] [CrossRef] - Radic, S. Parametric Signal Processing. IEEE J. Sel. Top. Quantum Electron.
**2012**, 18, 670–680. [Google Scholar] [CrossRef] - Peterson, A. Simulation and Testing of Wave-adaptive Modular Vessels. Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA, 2014. [Google Scholar]
- Fu, H.; Gu, Z.; Wang, Y. Ship Pitch Prediction Based on Bi-ConvLSTM-CA Model. J. Mar. Sci. Eng.
**2022**, 10, 840. [Google Scholar] [CrossRef] - Kim, C.; Ro, P.I.; Kim, H. Effect of the suspension structure on equivalent suspension parameters. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**1999**, 213, 457–470. [Google Scholar] [CrossRef] - Mauro, F.; Prpić-Oršić, J. Determination of a DP operability index for an offshore vessel in early design stage. Ocean. Eng.
**2020**, 195, 106764. [Google Scholar] [CrossRef] - Hossein, G.M.; Olszewski, H. Total Ship Operability—Review, Concept and Criteria. Pol. Marit. Res.
**2017**, 24, 74–81. [Google Scholar] [CrossRef] [Green Version] - Cong, Y.; Gan, H.; Wang, H.; Hu, G.; Liu, Y. Multiobjective Optimization of the Performance and Emissions of a Large Low-Speed Dual-Fuel Marine Engine Based on MNLR-MOPSO. J. Mar. Sci. Eng.
**2021**, 9, 1170. [Google Scholar] [CrossRef] - Smith, W.F.; Ayob, A.F.M.; Ray, T. The Design of High Speed Planing Craft Using an Optimization Framework. In Proceedings of the ASME 2012 International Mechanical Engineering Congress and Exposition, Houston, TX, USA, 9–15 November 2012; Volume 4: Dynamics, Control and Uncertainty, Parts A and B. pp. 11–20. [Google Scholar] [CrossRef]
- Jing, F.; Wang, S.; Guo, Z.; Ni, Y. A Simplified Panel Method (sPM) for Hydrodynamics of Air Cushion Assisted Platforms. J. Mar. Sci. Eng.
**2022**, 10, 1554. [Google Scholar] [CrossRef]

**Figure 10.**Comparison of simulated and experimental data. (

**a**) Heave displacement; (

**b**) Roll angle; (

**c**) Pitch angle.

**Figure 11.**Simulation animation screenshots with different wave impacts. (

**a**) Simulation with bow waves; (

**b**) Simulation with large heave motion.

**Figure 12.**Damping change simulation comparison with large heave motion. (

**a**) The amplitude of 0.1 m; (

**b**) Amplitude of 0.25 m; (

**c**) Amplitude of 0.4 m.

**Figure 13.**Stiffness change simulation comparison for large heave motion. (

**a**) The amplitude of 0.1 m; (

**b**) the amplitude of 0.25 m; (

**c**) the amplitude of 0.4 m.

**Figure 14.**Damping change simulation comparison with bow waves. (

**a**) The amplitude of 0.1 m; (

**b**) the amplitude of 0.25 m; (

**c**) the amplitude of 0.4 m.

**Figure 15.**Stiffness change simulations comparison with bow waves. (

**a**) The amplitude of 0.1 m; (

**b**) the amplitude of 0.25 m; (

**c**) the amplitude of 0.4 m.

**Figure 16.**Simulation animation with or without the spherical joint. (

**a**) With the spherical joint; (

**b**) Without the spherical joint.

**Figure 17.**Seakeeping criteria values with and without spherical joint. (

**a**) RMS of vertical acceleration; (

**b**) RMS of lateral acceleration; (

**c**) RMS of roll.

Symbol | Parameter | Dimensions |
---|---|---|

L | Overall length | 3.8 m |

L_{w} | Length of water plane | 3.5 m |

B | Beam | 1.88 m |

B_{h} | Hull diameter | 0.25 m |

W | Hull space | 1.63 m |

∇ | Displacement | 150–220 kg |

D | Average draft | 0.11–0.16 m |

m_{1} | Mass of the floating body | 53.5 kg |

m_{2} | Mass of the cabin | 43 kg |

I | Moment of inertia of the cabin | 22.25 kg·m^{2} |

L | Overall length | 3.8 m |

Stiffness Coefficient (N·m^{−1}) | Damping Coefficient (Ns·m^{−1}) | Gradient of Coefficient Change |
---|---|---|

4500 | 147 | −50% |

4500 | 221 | −25% |

4500 | 294 | reference value |

4500 | 368 | +25% |

4500 | 441 | +50% |

Stiffness Coefficient (N·m^{−1}) | Damping Coefficient (Ns·m^{−1}) | Gradient of Coefficient Change |
---|---|---|

2250 | 155 | −50% |

3375 | 190 | −25% |

4500 | 221 | reference value |

5625 | 245 | +25% |

6750 | 270 | +50% |

Stiffness Coefficient (N·m^{−1}) | Damping Coefficient (Ns·m^{−1}) | Gradient of Coefficient Change |
---|---|---|

4500 | 441 | reference value |

5625 | 490 | +25% |

6750 | 538 | +50% |

7875 | 582 | +75% |

9000 | 622 | +100% |

Seakeeping Elements | Merchant Ships | Navy Vessels | Fast Small Craft |
---|---|---|---|

RMS of vertical acceleration at forebridge | 0.05–0.275 g | 0.275 g | 0.65 g |

RMS of vertical acceleration at bridge | 0.15 g | 0.20 g | 0.275 g |

RMS of lateral acceleration at bridge | 0.12 g | 0.1 g | 0.1 g |

RMS of roll | 6.0° | 4.0° | 4.0° |

Probability of slamming | 0.01–0.03 | 0.03 | 0.03 |

Probability of deck wetness | 0.05 | 0.05 | 0.05 |

Seakeeping Elements | With Suspension | Without Suspension | Criteria |
---|---|---|---|

RMS of vertical acceleration at bridge | 0.05 g | 0.057 g | 0.275 g |

RMS of lateral acceleration at bridge | 0.052 g | 0.04 g | 0.1 g |

RMS of roll | 1.559° | 1.569° | 4.0° |

Seakeeping Elements | With Suspension | Without Suspension | Criteria |
---|---|---|---|

RMS of vertical acceleration at bridge | 0.124 g | 0.145 g | 0.275 g |

RMS of lateral acceleration at bridge | 0.085 g | 0.077 g | 0.1 g |

RMS of roll | 2.5543° | 2.5698° | 4.0° |

Amplitude of Bow Waves(m) | RMS of Pitch (°) | Amplitude of Heave (m) | ||||
---|---|---|---|---|---|---|

With Spherical Joint | Without Spherical Joint | Percentage Increase | With Spherical Joint | Without Spherical Joint | Percentage Reduction | |

0.05 | 0.3158 | 0.3097 | 1.97% | 0.0381 | 0.06256 | 39.10% |

0.1 | 0.6318 | 0.6094 | 3.68% | 0.07627 | 0.12513 | 39.05% |

0.15 | 0.9487 | 0.9294 | 2.08% | 0.11458 | 0.18766 | 38.94% |

0.2 | 1.267 | 1.24 | 2.18% | 0.153 | 0.2502 | 38.82% |

0.25 | 1.587 | 1.551 | 2.32% | 0.19183 | 0.3128 | 38.67% |

0.3 | 1.909 | 1.862 | 2.52% | 0.23107 | 0.3753 | 38.43% |

0.35 | 2.234 | 2.175 | 2.71% | 0.2706 | 0.4379 | 38.21% |

0.4 | 2.563 | 2.488 | 3.01% | 0.3108 | 0.5004 | 37.89% |

0.45 | 2.895 | 2.803 | 3.28% | 0.3516 | 0.563 | 37.55% |

0.5 | 3.233 | 3.119 | 3.66% | 0.3935 | 0.6256 | 37.10% |

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## Share and Cite

**MDPI and ACS Style**

Li, J.; Bai, X.; Li, Y.; Du, H.; Fan, F.; Li, S.; Li, Z.; Xiong, W.
Investigation of a Cabin Suspended and Articulated Rescue Vessel in Terms of Motion Reduction. *J. Mar. Sci. Eng.* **2022**, *10*, 1966.
https://doi.org/10.3390/jmse10121966

**AMA Style**

Li J, Bai X, Li Y, Du H, Fan F, Li S, Li Z, Xiong W.
Investigation of a Cabin Suspended and Articulated Rescue Vessel in Terms of Motion Reduction. *Journal of Marine Science and Engineering*. 2022; 10(12):1966.
https://doi.org/10.3390/jmse10121966

**Chicago/Turabian Style**

Li, Jiong, Xuesong Bai, Yang Li, Hongwang Du, Fangtao Fan, Shuaixian Li, Zhi Li, and Wei Xiong.
2022. "Investigation of a Cabin Suspended and Articulated Rescue Vessel in Terms of Motion Reduction" *Journal of Marine Science and Engineering* 10, no. 12: 1966.
https://doi.org/10.3390/jmse10121966