针对水下多缆(阵列)多体拖曳系统，给出了其动力学数学模型及其对应的数值求解方案，用以预报分析其在各种情况下的运动响应特性.模型由3部分组成：基于集中质量法给出了拖缆的运动控制方程；水下工作拖体因其为系统的关键部件而采用潜艇6自由度运动控制方程进行精确描述；而系统中另一个小型拖曳体因其尺度相对很小则简化为质量点融入拖缆的控制方程中.通过建立拖缆和拖体耦合边界条件将其耦合成一个整体，并采用4阶龙格库塔方法进行积分求解.最后针对4缆2拖曳体系统展开数值计算，研究了系统在不同情况下的运动响应特性，给出了一些规律性结论.
Aimed at the underwater multi-cable multi-body towed system, a mathematical model and the corresponding numerical solution are proposed to predict and analyze its dynamic characteristics in various conditions. The model consists of three parts: the governing equation of cables is given based on the lumped mass method; the underwater towed body, as a key part of the system, is accurately described by the 6 degree-of-freedom governing equations for submarines; the other tiny towed body in the system is simplified as a mass point and is incorporated into the cable node governing equation because of its small dimension. Coupling boundary conditions for towed cable and body are given to unite the three parts together, which is numerically solved by using the 4th order Runge-Kutta integration method. Finally, numerical simulations for a four-cable and two-body towed system are conducted to study its dynamic response in various conditions, and some conclusions are drawn from the results.
［1］王鲁军. 国外低频主动拖曳声呐发展现状和趋势［J］. 无人水下系统学报, 2018, 26(3): 193-199.
WANG Lujun. Current status and developing trend of low frequency active towed sonar abroad［J］. Journal of Unmanned Undersea Systems, 2018, 26(3): 193-199.
［2］实验室工作介绍. TowSimuX-水下拖曳系统动力学计算程序-Hengex@gmail.com ［EB/OL］. (2018-01-30) ［2019-03-08］ http://202.120.42.116: 6320/DT88888.
Research Introduction of Laboratory. TowSimuX-Dynamics and numerical simulation of underwater towed systems-Hengex@gmail.com［EB/OL］. (2018-01-30) ［2019-03-08］. http://202.120.42.116: 6320/DT88888.
［3］WANG F, HUANG G L, DENG D H. Steady state analysis of towed marine cables［J］. Journal of Shanghai Jiao Tong University (Science), 2008, 13(2): 239-244.
［4］HUANG S. Dynamics Analysis of three-dimensional marine cables ［J］. Ocean Engineering, 1994, 21(6): 587-605.
［5］庞师坤, 刘旌扬, 王健, 等. 二级深拖系统的回转运动特性［J］. 船舶工程, 2017, 39(9): 71-77.
PANG Sikun, LIU Jinyang, WANG Jian, et al. Motion characteristics of two-part towed system during towing ship turning maneuvers［J］. Ship Engineering, 2017, 39(9): 71-77.
［6］GOMES S C P, ZANELA E B, PEREIRA A E L. Automatic generation of dynamic models of cables ［J］. Ocean Engineering, 2016, 121: 559-571.
［7］PARK J, KIM N. Dynamics modeling of a semi-submersible autonomous underwater vehicle with a towfish towed by a cable［J］. International Journal of Naval Architecture and Ocean Engineering, 2015, 7(2): 409-425.
［8］苑志江, 金良安, 迟卫, 等. 海洋拖曳系统的船/缆/体耦合模型研究［J］. 船舶力学, 2016, 20(10): 1252-1261.
YUAN Zijiang, JIN Liang’an, CHI Wei, et al. Research on the coupling model of underwater towed system［J］. Journal of Ship Mechanics, 2016, 20(10): 1252-1261.
［9］郑智林, 苑志江, 金良安, 等. 舰船机动中拖曳系统建模与定深控制研究［J］. 兵器装备工程学报, 2016, 37(4): 106-110.
ZENG Ziling, YUAN Zijiang, JIN Liang’an, et al. Mathematic model and depth control of special underwater towed system during warship maneuvers［J］. Journal of Ordnance Equipment Engineering, 2016, 37(4): 106-110.
［10］WANG F, TU W M, DENG D H, et al. Dynamic effect research of cable-lead-in rod on towed system ［J］. Journal of Shanghai Jiao Tong University (Science), 2019, 26(6): 745-753.
［11］GONZALEZ F, DE LA PRADA A, LUACES A, et al. Real-time simulation of cable pay-out and reel-in with towed fishing gears ［J］. Ocean Engineering, 2017, 131: 295-307.
［12］付薇, 尹汉军, 许可, 等. 水下航行器近海底铺缆运动仿真研究［J］. 船舶力学, 2016, 20(10): 1244-1251.
FU Wei, YIN Hanjun, XU Ke, et al. Simulation research on cable laying of underwater vehicle sailing near seafloor［J］. Journal of Ship Mechanics, 2016, 20(10): 1244-1251.
