﻿ 基于仿生学的舰船外型设计研究
 舰船科学技术  2024, Vol. 46 Issue (10): 83-86    DOI: 10.3404/j.issn.1672-7649.2024.10.014 PDF

Research on ship exterior design based on bionics
WANG Qi
Zhengzhou University of Industrial Technology, Zhengzhou 450000, China
Abstract: This article studies bionics, with a focus on analyzing the kinematics and dynamics of dolphin tail swinging. The wave amplitude curve of the fish body is presented, and the motion curve of the dolphin is analyzed. At the same time, the transient velocity change curve of the dolphin is studied; Studied the design methods of ship profiles, with a focus on analyzing three design methods: fusion technology, superimposed disturbance surface technology, and cross-sectional movement technology, and explored the ship profile design method based on NURBS curves; Finally, simulation design was carried out for the optimization of ship shape, and the simulation results before and after ship shape optimization were provided. This study contributes to the rapid development of ship exterior design technology in China.
Key words: biomimetics     ships     appearance design
0 引　言

1 仿生学 1.1 海豚尾部摆动运动学分析

 $\left\{ {\begin{array}{*{20}{l}} {y = \left( {{c_1}x + {c_2}{x^2}} \right)\sin \left( {kx + \omega t} \right)}，\\ {k = \dfrac{{2{\text{π}} }}{\lambda } = \dfrac{{2{\text{π}} R}}{L}} ，\\ {\omega = 2{\text{π}} f} 。\end{array}} \right.$ (1)

 图 1 海豚鱼体波幅曲线 Fig. 1 Dolphin fish body wave amplitude curve

 ${Y_{\rm{body}}}\left( {x,t} \right) = {H_{\max }}g\left( x \right)\sin \left( {2{\text{π}} ft} \right)\text{。}$ (2)

 $g\left( x \right) = 0.21 - 0.66x + 1.1{x^2} + 0.35{x^8}。$ (3)

 图 2 海豚运动曲线 Fig. 2 Dolphin movement curve
 $g\left(x\right)=0.1-1.3x-2x^2\text{。}$ (4)

 $\left\{ {\begin{array}{*{20}{l}} {x = Ut - d\cos \left[ {\left( {\dfrac{{2{\text{π}} fH}}{U} - {\alpha _{\max }}} \right)\sin \left( {2{\text{π}} ft + \psi } \right)} \right]}，\\ {y = H\sin \left( {2{\text{π}} ft} \right) - d\sin \left[ {\left( {\dfrac{{2{\text{π}} fH}}{U} - {\alpha _{\max }}} \right)\sin \left( {2{\text{π}} ft + \psi } \right)} \right]}。\end{array}} \right.$ (5)

 ${y}_{尾鳍}=H\mathrm{sin}\left(2{\text{π}} ft\right)-\left(x-{x}_{\alpha }\right)\mathrm{sin}\left(2{\text{π}} ft+\psi \right) \text{，}$ (6)
 $\left\{\begin{array}{*{20}{l}}Y\mathrm{_{body}}\left(x_{\alpha},t\right)=a\left(t\right)A\left(x_a\right)\sin\left[2\text{π}\left(\dfrac{t}{T}-\dfrac{x_a}{\lambda}\right)\right]，\\ a\left(t\right)=\left\{\begin{array}{*{20}{l}}\dfrac{t}{T}-\dfrac{1}{2\text{π}}\sin\left(\dfrac{2\text{π}t}{T}\right)，0\leqslant t\leqslant T，\\ 1，t > T。\end{array}\right.\end{array}\right.$ (7)
1.2 海豚尾部摆动动力学分析

 ${F_D} = \frac{1}{2}{C_D}{\rho _f}{\mu ^2}S。$ (8)

 ${F_i}\Delta t = {m_{ft}}{v_{\alpha i}}\text{。}$ (9)

 ${m_{ft}} = {\rho _f}{V_i}\text{，}$ (10)
 ${v_{\alpha i}} = 2{\text{π}} f{A_i}\cos \left( {2{\text{π}} ft} \right)\text{，}$ (11)
 $\left\{ {\begin{array}{*{20}{l}} {{l_i} = {A_i}\sin \left( {\omega t} \right)}，\\ {{\xi _i} = {\psi _i}\sin \left( {\omega t - {\phi _i}} \right)} 。\end{array}} \right.$ (12)

 $\left\{ {\begin{array}{*{20}{l}} {M{{\ddot X}_C} = F - {F_D}} ，\\ {F = \displaystyle\sum\limits_{i = 1}^4 {{F_i}} }，\\ {u = {{\dot X}_C}} 。\end{array}} \right.$ (13)

 图 3 瞬态速度变化曲线 Fig. 3 Transient velocity variation curve
2 船舶型线设计方法

 $x_i^k = \sum\limits_{j = 1}^N {{w_j}x_i^j} \text{。} \\$ (14)

 $\sum\limits_{j = 1}^N {{w_j} = 1} \text{。}$ (15)

 ${\xi _n}\left( {u,v} \right) = \sum\limits_{i = 0}^{{N_n} - 1} {\sum\limits_{j = 0}^{{M_n} - 1} {{J_{{N_x},i}}\left( u \right)} } {K_{M,j}}\left( v \right){\xi _{i,j}}\text{，}$ (16)
 ${J_{N,i}} = \left( {\begin{array}{*{20}{c}} {{N_x} - 1} \\ i \end{array}} \right){\left( {1 - u} \right)^{{N_x} - 1 - i}}{u^i}\text{，}$ (17)
 ${K_{{N_x},j}} = \left( {\begin{array}{*{20}{c}} {{M_x} - 1} \\ j \end{array}} \right){\left( {1 - v} \right)^{{M_x} - 1 - j}}{v^i}\text{。}$ (18)

 ${\wp _B} = \left( {{\xi _B},{\eta _B},{\zeta _B}} \right)\text{，}$ (19)
 ${X_{{\mathrm{mod}} }} = {X_0} + {\wp _B}\text{。}$ (20)

 $u = [{u_0},{u_1},...,{u_{n + k + 1}}]\text{，}$ (21)
 $\vec p\left( u \right) = \frac{{\displaystyle\sum\limits_{i = 0}^n {{w_i}{{\bar d}_i}{N_{i,k}}\left( u \right)} }}{{\displaystyle\sum\limits_{i - 0}^n {{w_i}{N_{i,k}}\left( u \right)} }}\text{。}$ (22)

 $\vec p\left( {u,v} \right) = \frac{{\displaystyle\sum\limits_{i = 0}^n {\displaystyle\sum\limits_{j = 0}^m {{w_{i,j}}{{\vec d}_{ij}}{N_{i,k}}\left( u \right){N_{j,l}}\left( v \right)} } }}{{\displaystyle\sum\limits_{i = 0}^n {\displaystyle\sum\limits_{j = 0}^m {{w_{ij}}{N_{i,k}}\left( u \right){N_{j,l}}\left( v \right)} } }}\text{。}$ (23)

 ${{\mathrm{d}}^2}z = \frac{{{\partial ^2}z}}{{\partial {x^2}}}{{{\mathrm{d}}}}{x^2} + 2\frac{{{\partial ^2}z}}{{\partial x\partial y}}{\rm{d}}x{\rm{d}}y + \frac{{{\partial ^2}z}}{{\partial {y^2}}}{\rm{d}}{y^2}\text{。}$ (24)

 $p = \sum\limits_{i = 1}^n {{C_i} \times {P_i}} \text{。}$ (25)

 $\sum\limits_{i = 1}^n {{C_i} = 1} \text{。}$ (26)
3 船舶外型优化仿真设计

 ${R_t} = {R_{vp}} + {R_f} + {R_w}\text{。}$ (27)

 ${R_f} + {R_{vp}} = {R_f}(1 + k)\text{，}$ (28)
 $1 + k = {c_1}\left\{ {0.93 + {c_2}{{\left( {\frac{B}{{{L_R}}}} \right)}^{0.93}}{{\left( {0.95 - {C_p}} \right)}^{ - 0.52}}} \right\}\text{。}$ (29)

 $\frac{{{L_R}}}{L} = 1 - {C_p} + \frac{{0.06{C_p}{l_{cb}}}}{{4{C_p} - 1}}\text{。}$ (30)

 $\Delta {C_f} = \left[ {105 \times {{\left( {\frac{{{k_s}}}{L}} \right)}^{\frac{1}{3}}} - 0.64} \right] \times {10^{ - 3}}\text{。}$ (31)

 图 4 船舶舷侧纵切波形曲线 Fig. 4 Ship side longitudinal shear waveform curve
 ${R_w} = {C_w} \cdot \frac{1}{2}\rho {V^2}S\text{。}$ (32)

 图 5 不同航速下阻力的变化曲线 Fig. 5 The variation curve of resistance under different sailing speeds

 图 6 不同航速下阻力增加比例的变化曲线 Fig. 6 The variation curve of the proportion of resistance increase at different speeds
4 结　语

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