﻿ 二阶stokes波作用下水下机器人载体结构稳定性分析
 舰船科学技术  2022, Vol. 44 Issue (14): 77-82    DOI: 10.3404/j.issn.1672-7649.2022.14.018 PDF

Stability analysis of an underwater robot carrier structure under the action of second-order stokes waves
HUANG Jia-ning, HAN Jiang-gui
School of Power Engineering, Naval University of Engineering, Wuhan 430063, China
Abstract: Based on the modular design idea, we design an underwater robot carrier structure with truss structure as the main body and can carry and transport underwater robots and auxiliary equipment for underwater operation. The carrier structure is required to be not only safe, stable and reliable but also simple and practical and easy to store in a complex and diverse marine environment with the combined effects of wind, waves and currents. According to the wave research report of Coastal Dynamics, the second order stokes wave parameters with high frequency are selected, the wave disturbance at the entrance is realized by Ansys based on the boundary wave making method, the free liquid surface is tracked by VOF calculation method and the second order stokes wave is numerically simulated by the damping wave elimination technique to complete the simulation analysis of the carrier structure under the action of wave current. In addition, the wave force is applied to the carrier structure and the transient dynamic analysis is carried out. The displacement and stress time curves are obtained when the suction cup is not installed and when the suction cup is installed, and the extreme values of the curves are analyzed to verify the stability and reliability of the carrier structure of the underwater robot. The stability and reliability of the underwater robot carrier structure are verified.
Key words: underwater robots     second order stokes     wave current forces     wave forces
0 引　言

1 水下机器人载体结构设计

 图 1 水下机器人载体总体结构图 Fig. 1 Overall structure of the platform

 图 2 水下机器人载体结构分部件图 Fig. 2 Overall structure of the platform
2 三维stokes数值波浪建立 2.1 二阶stokes波浪理论

 $\begin{split} \varphi \left( {x,y,t} \right) = &\frac{{H\omega }}{{2k}}\left[\frac{{\cosh k\left( {y + d} \right)}}{{\sinh kd}} \times \sin \left( {kx - \omega t} \right)+ \right.\\ &\left. \frac{3}{{16}}Hk\frac{{\cosh 2k\left( {y + d} \right)}}{{{{\sinh }^4}kd}} \times \sin \left( {2kd - 2\omega t} \right)\right] 。\end{split}$ (1)

 $\rho\left(\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}\right)=S_{m} 。$ (2)

N-S方程：

 $\left\{ \begin{gathered} \rho \left( {\frac{{\partial u}}{{\partial t}} + u\frac{{\partial u}}{{\partial x}} + v\frac{{\partial u}}{{\partial y}}} \right) = - \frac{{\partial p}}{{\partial x}} + \mu \left( {\frac{{{\partial ^2}u}}{{\partial {x^2}}} + \frac{{{\partial ^2}u}}{{\partial {y^2}}}} \right) + {S_x} ，\\ \rho \left( {\frac{{\partial v}}{{\partial t}} + u\frac{{\partial v}}{{\partial x}} + v\frac{{\partial v}}{{\partial y}}} \right) = - \frac{{\partial p}}{{\partial y}} - \rho g + \mu \left( {\frac{{{\partial ^2}v}}{{\partial {x^2}}} + \frac{{{\partial ^2}v}}{{\partial {y^2}}}} \right) + {S_y} 。\\ \end{gathered} \right.$ (3)

2.2 波浪水槽建立与结果分析

 图 3 三维数值波浪水槽示意图 Fig. 3 Diagram of 3D numerical wave flume

 图 4 添加消波后波浪的历时演化过程 Fig. 4 The diachronic evolution of waves after wave elimination is added

 图 5 距离入口边界10 m处波面时程曲线 Fig. 5 Time history curve of wave surface at 10 m away from the entrance boundary

 图 6 距离入口边界20 m处波面时程曲线 Fig. 6 Time history curve of wave surface at 20 m away from the entrance boundary

 图 7 距离入口边界40 m处波面时程曲线 Fig. 7 Time history curve of wave surface at 40 m away from the entrance boundary

3 载体结构波流力仿真计算

3.1 波浪力仿真计算

 图 8 计算域模型 Fig. 8 Computational domain model

 图 9 波浪作用下的液面图 Fig. 9 Liquid level diagram under wave action

 图 10 桁架结构水平波浪力时程曲线 Fig. 10 Time history curve of horizontal wave force of truss structure

3.2 水流力仿真计算

 图 11 水流作用下的液面图 Fig. 11 Liquid level diagram under the action of water flow

 图 12 纵向水流力时程曲线 Fig. 12 Time history curve of longitudinal flow force

4 波流作用下载体结构响应 4.1 载体结构模态分析

Ansys的模态分析是线性分析，任何非线性特性即使定义了也将被忽略[20]，因此利用Block Lanzcos法特征值求解器提取模态特征值，采用一组向量来实现Lanzcos递归的计算，实现对载体结构的模态分析，获得结构的振型并与波浪载荷的固有频率进行对比，分析结构发生共振的可能性。安装吸盘与未安装吸盘时一阶模态分析模型结果分别如图13图14所示。

 图 13 安装吸盘一阶振型 Fig. 13 Installation of suction cups Mode 1

 图 14 未安装吸盘一阶振型 Fig. 14 without suction cups installed Mode 1

4.2 载体结构瞬态动力分析

 图 15 未安装吸盘时载体结构底端总位移 Fig. 15 Total displacement of the bottom of the carrier structure without suction cup

 图 16 未安装吸盘时锁紧连接处等效应力 Fig. 16 Equivalent stress of locking joint without suction cup

 图 17 安装吸盘时载体结构底端总位移 Fig. 17 Total displacement of the bottom of the carrier structure when installing the suction cup

 图 18 安装吸盘时垂直桁架安装吸盘处等效应力 Fig. 18 Equivalent stress of suction cup in vertical truss

5 结　语

1）无论是否安装吸盘，载体结构底端位移值在加载初期都表现出比较强烈的波动且在某一时刻达到最大，之后位移逐渐表现为稳定周期性变化。位移曲线和stokes波的波浪力时程曲线形状相似并且位移与波浪力的关系符合载体结构材料的线弹性特征。因此，水下机器人载体结构材料选择上要保证有足够的弹性性能。

2）载体结构关键部位的应力值在加载初期表现出比较强烈的波动，之后才逐渐稳定，而未安装吸盘时的应力极值远大于安装吸盘时的应力极值，即从另一方面说明安装吸盘能有效地抵抗类似stokes波等的冲击作用，对于整个结构的安全性和稳定性具有重要作用。

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