﻿ 三体船运动与波浪载荷的伪共振问题研究
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 哈尔滨工程大学学报  2019, Vol. 40 Issue (6): 1051-1057  DOI: 10.11990/jheu.201804087 0

### 引用本文

ZOU Jian, WANG Fanchao, LI Hui, et al. Pseudoresonance in trimaran motion and wave load estimation[J]. Journal of Harbin Engineering University, 2019, 40(6), 1051-1057. DOI: 10.11990/jheu.201804087.

### 文章历史

1. 哈尔滨工程大学 船舶工程学院, 黑龙江 哈尔滨 150001;
2. 中国船舶工业集团公司第七〇八研究所, 上海 200011

Pseudoresonance in trimaran motion and wave load estimation
ZOU Jian 1, WANG Fanchao 2, LI Hui 1, DENG Baoli 1, REN Huilong 1, HU Xuecong 1
1. School of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China;
2. NO. 708 Research Institute of CSSC, Shanghai 200000, China
Abstract: Pseudoresonance will occur at some discrete frequencies when the zero-velocity linear potential flow theory is applied to calculate trimaran motion and wave loads. This work investigates the characteristics of the variation in pseudoresonance under different environmental conditions and different side-hull layouts and the characteristics of radiation wave propagation under side-hull interference. The extended boundary integral equation method is adopted to solve pseudoresonance. In contrast with experimental methods, the improved method can address pseudoresonance effectively and can be conveniently employed for calculation in engineering projects.
Keywords: trimaran    motion    wave loads    main-hull    side-hulls    pseudoresonance    radiation wave    boundary integral    viscous dampingg

1 考虑粘性修正的三体船伪共振处理方法

 (1)

 \begin{aligned} \phi(x, y, z)=& \phi_{I}(x, y, z)+\phi_{D}(x, y, z)+\\ & \sum\limits_{j=1}^{6} \dot{\zeta}_{j} \phi_{j}(x, y, z) \end{aligned} (2)

 $\begin{array}{l} [L]{\nabla ^2}{\phi _j}(x, y, z) = 0\\ [F]\left\{ {\begin{array}{*{20}{l}} { - {\omega ^2}{\phi _j} + g\frac{{\partial {\phi _j}}}{{\partial z}} = 0, }&{自由面{F_1}}\\ {g\frac{{\partial {\phi _j}}}{{\partial z}} - \left( {{\omega ^2} - i\upsilon \omega } \right){\phi _j} = 0, }&{自由面{F_2}} \end{array}} \right.\\ [S]\left\{ {\begin{array}{*{20}{l}} {{{\left. {\frac{{\partial {\phi _j}}}{{\partial n}}} \right|}_{S0}} = {n_j}}\\ {\frac{{\partial {\phi _7}}}{{\partial n}} = - \frac{{\partial {\phi _I}}}{{\partial n}}} \end{array}} \right.\\ [B]\mathop {\lim }\limits_{z \to - \infty } \nabla {\phi _j} = 0\\ [R]\mathop {\lim }\limits_{R \to \infty } \sqrt R \left( {\frac{{\partial {\phi _j}}}{{\partial R}} - ik{\phi _j}} \right) = 0 \end{array}$ (3)

 $\phi_{j}(P)=\iint\limits_{S_{+}+F_{2}} \sigma(Q) G(P, Q) \mathrm{d} s$ (4)

 $\left\{ {\begin{array}{*{20}{l}} {2\pi \sigma (P) + \frac{{{\text{i}}\upsilon \omega }}{g}\iint\limits_{{F_2} + {S_0}} \sigma (Q)G(P, Q){\text{d}}s = 0, } \\ {\;\;\;P \in {F_2}} \\ {2\pi \sigma (P) + \iint\limits_{{F_2} + {S_0}} \sigma (Q)\frac{{\partial G(P, Q)}}{{\partial n}}{\text{d}}s = \frac{{\partial {\phi _j}(P)}}{{\partial n}}, } \\ {\;\;\;P \in {S_0}} \end{array}} \right.$ (5)

 $F_{i}=\rho \iint\limits_{s}\left(\mathrm{i} \omega+U \frac{\partial}{\partial x}\right)\left(\phi_{I}(x, y, z)+\phi_{D}(x, y, z) n_{i}\right) \mathrm{d} S$ (6)

 $\begin{array}{c}{\sum\limits_{j=1}^{6} D_{i j} \zeta_{j}=-\rho \iint\limits_{s} \sum\limits_{j=1}^{6}\left(\mathrm{i} \omega+U \frac{\partial}{\partial x}\right) \zeta_{j} \phi_{j}(x, y, z) n_{j} \mathrm{d} S=} \\ {\sum\limits_{j=1}^{6}\left(\omega^{2} A_{i j}+\mathrm{i} \omega B_{i j}\right) \zeta_{j}}\end{array}$ (7)

 $\sum\limits_{j = 1}^6 {\left[ { - {\omega ^2}\left( {M + {A_{ij}}} \right) - {\rm{i}}\omega {B_{ij}} + {C_{ij}}} \right]} {\zeta _j} = {F_i}$ (8)

2 三体船伪共振特性分析

2.1 船体水动力模型网格收敛性分析

 Download: 图 3 三体船水动力模型与试验模型 Fig. 3 Hydrodynamic model and test modle of the trimaran
 Download: 图 4 垂荡、纵摇运动随不同面元数变化 Fig. 4 Heave and pitch variation with different grids
2.2 三体船运动与载荷响应伪共振特性分析

 Download: 图 5 垂荡、纵摇运动和垂向弯矩理论与试验结果(12 kn) Fig. 5 Theoretical and experimental results of heave, pitch and VBM (12 kn)

 Download: 图 6 0、12 kn航速时各浪向下垂荡运动 Fig. 6 Heave in different directions at 0 and 12 knots
 Download: 图 7 0、12 kn航速时各浪向下纵摇运动 Fig. 7 Pitch in different directions at 0 and 12 knots
 Download: 图 8 0、12 kn航速时各浪向下横摇运动 Fig. 8 Roll in different directions at 0 and 12 knots

2.3 片体布置位置对伪共振的影响

 Download: 图 9 三体船片体的不同布置位置 Fig. 9 Different layouts of side-hulls of the trimaran
 Download: 图 10 垂荡和纵摇运动受片体横向位置的影响(12 kn) Fig. 10 Heave and pitch with different transversely position of side-hulls (12 kn)

 Download: 图 11 垂荡和纵摇运动受片体纵向位置的影响(12 kn) Fig. 11 Heave and pitch with different longitudinally position of side-hulls (12 kn)
2.4 辐射与绕射波面特性分析

 Download: 图 12 自由面上辐射波和绕射波波形 Fig. 12 Wave profile of radiation and diffraction wave on free surface of

3 三体船运动与载荷响应的伪共振修正

 Download: 图 13 添加不同粘性阻尼后三体船运动响应以及兴波图 Fig. 13 Motion response and wave profile of trimaran after adding different viscous-coefficients

4 结论

1) 对于本文所研究的伪共振问题，航速效应对伪共振的峰值大小有很大影响；在有航速情况下，伪共振的出现浪向角趋于迎浪到横浪之间；三体船的船型布置是影响伪共振的峰值频率变化的主要因素。

2) 伪共振的发生主要是来自纵摇运动与辐射波的耦合作用，而垂荡运动响应上出现伪共振更多的是受到纵摇运动的影响。

3) 拓展的积分方程方法能够有效的用于解决伪共振问题且对于其他频率段的计算结果影响不大，根据本文计算经验，最佳粘性系数一般取为0.1~0.5。

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