# Laboratory Experimental Investigation on the Hydrodynamic Responses of an Extra-Large Electrical Platform in Wave and Storm Conditions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Model Similarity

_{ρ}·λ

_{A}·λ

^{3}·λ

_{u}·λ

_{t}

^{−2}= λ

_{I}·λ

_{E}·λ

_{u}·λ

^{−3},

_{ρ}is density scale, λ is geometric scale, λ

_{u}is deformation scale, λ

_{E}is elastic modulus, λ

_{t}is time scale, λ

_{A}is sectional area scale, and λ

_{I}is sectional moment of inertia scale.

_{t}

^{2}= λ

^{4}·λ

_{ρ}·λ

_{E}

^{−1}·λ

_{r}

^{−2},

_{r}is radius of inertia scale.

_{g}= 1, thus,

_{t}= λ

^{0.5},

^{3}·λ

_{r}

^{−2}= λ

_{E},

#### 2.2. Mechanical Test of the Experimental Material

^{3}. Standard specimens with thickness of 3 mm, 4 mm, 5 mm, and 10 mm were produced with 4 duplicates for each specimen. A universal testing machine was used to determine the static elastic modulus and Poisson ratio of plexiglass by uniaxial tensile test. The average values of static modulus and Poisson ratio of all specimens were taken as the material parameters of plexiglass. The static elastic modulus and Poisson ratio of plexiglass were 2.62 GPa and 0.42, respectively. For the dynamic model test of the electrical platform in this study, the dynamic elasticity modulus of the material should also be considered. The dynamic elasticity modulus can be calculated by measuring the fundamental frequency of a cantilever beam with rectangular section according to the formula as follow.

^{2}ρAL

^{4}f

^{2}/(3.515

^{2}I),

#### 2.3. Experimental Model Design

#### 2.4. Experimental Set-Up

#### 2.5. Experimental Conditions

## 3. Results

#### 3.1. Strain Response of Electrical Platform

#### 3.1.1. The Electrical Platform in Regular Waves

#### 3.1.2. The Electrical Platform in Storm Condition

#### 3.2. Acceleration Response of Electrical Platform

#### 3.2.1. The Electrical Platform in Regular Waves

#### 3.2.2. The Electrical Platform in Storm Condition

## 4. Discussion

#### 4.1. Effect of Water Depth on Strain Response

#### 4.2. Effect of Attack Angle on Strain Response

#### 4.3. Effect of Environmental Loads on Strain Response

#### 4.4. Effect of Water Depth on Acceleration Response

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**The experimental layout of acceleration sensors. (

**a**) Acceleration sensor; (

**b**) Acceleration sensors on the platform.

**Figure 6.**Time-series of the strain response of strain gauges at measurement position S5 in waves. Wave condition: H = 0.10 m and T = 1.6 s.

**Figure 7.**Time-series of the strain response at various measurement positions in waves. Wave condition: H = 0.15 m and T = 1.4 s.

**Figure 8.**The structural strains at various measurement positions in waves. (

**a**) Variation with wave height when wave period T = 1.6 s; (

**b**) Variation with wave period when wave height H = 0.15 m.

**Figure 9.**Time-series of the strain response at various measurement positions in storm conditions. (

**a**) S1; (

**b**) S2; (

**c**) S3; (

**d**) S4.

**Figure 10.**The peak accelerations at various measurement positions in waves. (

**a**) Variation with wave height when wave period T = 1.6 s; (

**b**) Variation with wave period when wave height H = 0.15 m.

**Figure 11.**Frequency-domain comparison of acceleration responses at measurement positions J7 and J8 in waves. (

**a**) J7; (

**b**) J8.

**Figure 12.**Time-series of the acceleration response at various measurement positions in wave condition A5. (

**a**) J1, J2, J3; (

**b**) J4, J5, J6; (

**c**) J7, J8; (

**d**) J3, J6, J7.

**Figure 13.**Frequency domain comparison of acceleration responses at various measurement positions in storm condition C2. (

**a**) J2 and J6; (

**b**) J7 and J8.

**Figure 14.**Time-series of the acceleration response at various measurement positions in storm condition C2. (

**a**) J1, J2, J3; (

**b**) J4, J5, J6; (

**c**) J7, J8; (

**d**) J3, J6, J7.

**Figure 15.**Structural strain responses at various measurement positions of the electrical platform with different water depths in waves for wave period of 1.6 s. (

**a**) S1; (

**b**) S2; (

**c**) S3; (

**d**) S4; (

**e**) S5; (

**f**) S6.

**Figure 16.**Structural strain responses at various measurement positions of the electrical platform with various attack angles in waves for wave period of 1.6 s. (

**a**) S1; (

**b**) S2; (

**c**) S3; (

**d**) S4; (

**e**) S5; (

**f**) S6.

**Figure 17.**Time-series of the strain response at measurement position S2 in both wave and storm conditions.

**Figure 18.**Structural peak accelerations at various measurement positions of the electrical platform with different water depths in waves for wave period of 1.6 s at attack angle of 90°. (

**a**) J1; (

**b**) J2; (

**c**) J3; (

**d**) J4; (

**e**) J5; (

**f**) J6; (

**g**) J7; (

**h**) J8.

Parameter | Similarity | Similar Scale |
---|---|---|

Length | λ | 60 |

Area | λ_{A} | 1120.7 |

Volume | λ·λ_{A} | 67,241 |

Density | λ_{ρ} = 1 | 1 |

Mass | λ_{ρ}·λ·λ_{A} | 67,241 |

Speed | λ^{0.5} | 7.746 |

Acceleration | λ_{g} = 1 | 1 |

Time | λ^{0.5} | 7.746 |

Frequency | λ^{−0.5} | 0.129 |

Force | λ^{3} | 60^{3} |

Moment | λ^{4} | 60^{4} |

Moment of area | λ_{A}·λ_{r}^{2} | 4.59e6 |

Moment of mass | λ·λ_{A}·λ_{r}^{2} | 2.76e8 |

Stress | λ^{4}·λ_{D}·λ_{A}^{−1}·λ_{r}^{−2} | 176.3 |

Member Type | Model Number | Sectional Dimension (mm) | Section for Model |
---|---|---|---|

Box beam | B3000 | 59.1 × 23 | Rectangular section (Height × Width) |

I-beam | H2000 | 45.5 × 8.6 | |

H1500 | 34.2 × 6.8 | ||

H1200 | 27.6 × 6.4 | ||

H1000 | 22.8 × 5.1 | ||

H800 | 18.1 × 3.8 | ||

Pipe | P2000 × 50 | 32 × 3 | Pipe (Outside diameter × Thickness) |

P1500 × 40 | 25 × 2 | ||

P1000 × 30 | 22 | Solid bar (Diameter) | |

P800 × 24 | 18 |

Member Type | Model Number | Sectional Dimension (mm) | Section for Model |
---|---|---|---|

Pipe | P2000 × 50 | 32 × 3 | Pipe (Outside diameter × Thickness) |

P1500 × 40 | 25 × 2 | ||

P1200 × 40 | 20 × 2 | ||

P2800 × 70 | 45 × 5 | ||

P2600 × 60 | 45 × 3 | ||

P2900 × 135 | 50 × 5 |

Test Number | Wave Height (m) | Wave Period (s) |
---|---|---|

A1 | 0.05 (3) ^{1} | 1.6 (12.4) |

A2 | 0.10 (6) | 1.6 (12.4) |

A3 | 0.15 (9) | 1.0, 1.2, 1.4, 1.6, 1.8 (7.7, 9.3, 10.8, 12.4, 13.9) |

A4 | 0.20 (12) | 1.6 (12.4) |

A5 | 0.25 (15) | 1.6 (12.4) |

^{1}The values in parentheses represent the prototype values.

Test Number | Significant Wave Height (m) | Significant Wave Period (s) |
---|---|---|

B1 | 0.15 (9) | 1.6 (12.4) |

B2 | 0.20 (12) | 1.8 (13.9) |

Test Number | Wind Speed (m/s) | Current Speed (m/s) | Irregular Wave |
---|---|---|---|

C1 | 4.6 (36) | 0.226 (1.75) | H_{s} = 0.15 mT _{p} = 1.6 s |

C2 | 6.6 (51.5) | 0.258 (2) | H_{s} = 0.20 mT _{p} = 1.8 s |

Wave Condition | Measuring Point | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

H0.05_T1.6 | 1.7 | 2.3 | 0.5 | 0.13 | 1.9 | 0.53 |

H0.10_T1.6 | 3.4 | 5.2 | 0.65 | 0.35 | 3.6 | 1.2 |

H0.15_T1.0 | 1.8 | 5.1 | 1.2 | 0.8 | 3.7 | 2.8 |

H0.15_T1.2 | 2.1 | 6.5 | 0.9 | 0.5 | 3.7 | 3.3 |

H0.15_T1.4 | 3.9 | 7.7 | 1.1 | 0.6 | 4.9 | 3 |

H0.15_T1.6 | 5.3 | 8.2 | 1.2 | 0.81 | 6 | 2.4 |

H0.15_T1.8 | 6.4 | 9.2 | 1.7 | 1.3 | 6.7 | 2.2 |

H0.20_T1.6 | 8.2 | 12.1 | 1.9 | 1.5 | 8.8 | 3.8 |

H0.25_T1.6 | 10.6 | 16.2 | 3.2 | 2.5 | 11.8 | 5.3 |

**Table 8.**Peak values of acceleration response at various measurement positions in waves (unit: m/s

^{2}).

Wave Condition | Measuring Point | |||||||
---|---|---|---|---|---|---|---|---|

J1 | J2 | J3 | J4 | J5 | J6 | J7 | J8 | |

H0.05_T1.6 | 0.0197 | 0.024 | 0.0251 | 0.0121 | 0.0044 | 0.0047 | 0.0035 | 0.0075 |

H0.10_T1.6 | 0.0336 | 0.0644 | 0.0691 | 0.0368 | 0.0082 | 0.0083 | 0.0065 | 0.0055 |

H0.15_T1.0 | 0.1078 | 0.2110 | 0.2087 | 0.1063 | 0.0226 | 0.0219 | 0.0208 | 0.0174 |

H0.15_T1.2 | 0.0722 | 0.1510 | 0.167 | 0.0619 | 0.0173 | 0.0146 | 0.0119 | 0.0155 |

H0.15_T1.4 | 0.0630 | 0.1420 | 0.1561 | 0.056 | 0.0132 | 0.0126 | 0.0095 | 0.0118 |

H0.15_T1.6 | 0.0577 | 0.1296 | 0.1313 | 0.0601 | 0.0134 | 0.0141 | 0.0124 | 0.0111 |

H0.15_T1.8 | 0.0510 | 0.1081 | 0.1118 | 0.0552 | 0.0112 | 0.0146 | 0.0106 | 0.0104 |

H0.20_T1.6 | 0.0715 | 0.1369 | 0.1624 | 0.077 | 0.0163 | 0.0146 | 0.0126 | 0.0131 |

H0.25_T1.6 | 0.078 | 0.1505 | 0.1901 | 0.075 | 0.0173 | 0.0149 | 0.0152 | 0.0178 |

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**MDPI and ACS Style**

Zhang, D.-L.; Bi, C.-W.; Wu, G.-Y.; Zhao, S.-X.; Dong, G.-H.
Laboratory Experimental Investigation on the Hydrodynamic Responses of an Extra-Large Electrical Platform in Wave and Storm Conditions. *Water* **2019**, *11*, 2042.
https://doi.org/10.3390/w11102042

**AMA Style**

Zhang D-L, Bi C-W, Wu G-Y, Zhao S-X, Dong G-H.
Laboratory Experimental Investigation on the Hydrodynamic Responses of an Extra-Large Electrical Platform in Wave and Storm Conditions. *Water*. 2019; 11(10):2042.
https://doi.org/10.3390/w11102042

**Chicago/Turabian Style**

Zhang, Dong-Liang, Chun-Wei Bi, Guan-Ye Wu, Sheng-Xiao Zhao, and Guo-Hai Dong.
2019. "Laboratory Experimental Investigation on the Hydrodynamic Responses of an Extra-Large Electrical Platform in Wave and Storm Conditions" *Water* 11, no. 10: 2042.
https://doi.org/10.3390/w11102042