基于风力、水流力和水深的系泊系统的模型研究

Model study of mooring system based on wind,water flow and water depth

本文针对2016年全国大学生数学建模A题数据,熟练运用了物理学中的静力学知识,通过对系泊系统的组成构件(浮标、钢桶、钢管、锚链)的受力分析,利用力学平衡原理,得到一系列平衡力系的方程,较为完整的分析了各部件之间的力学关系,并使用软件求解模型计算出模型的各参数数值以及锚链形状的悬链线方程,建立了基于风力、水流力和水深的系泊系统模型,并根据该模型在海水速度为1.5 m/s,风速为36 m/s时,分别计算出了水深为16 m和水深为20 m处,重物球的最小质量分别为3 802 kg和4 800kg和悬链线的长度至少分别为22.05 m和28 m,才能使得整个系统平衡时,满足在锚点的切线与海床的夹角不超过16°、铁桶的倾斜角度不超过5°的条件。

This paper is based on the data of the national mathematics modeling A of 2016,and skillfully uses the static knowledge in physics. Through the analysis of the components of the mooring system（ buoys,steel drums,steel pipes,anchor chains）,using the principle of mechanical balance,a series of equations of equilibrium force system are obtained,and the mechanical relationship between the components is analyzed. The software solves the model to calculate the parameters of the model and the catenary equation of the shape of the anchor chain. Based on the mooring system model of wind,water flow and water depth,according to the model,when the sea speed is 1. 5 m/s and the wind speed is 36 m/s,the water depth is 16 m and the water depth is 20 m. The minimum mass of the heavy ball is 3 802 kg and 4 800 kg and the length of the catenary is at least 22. 05 m and 28 m respectively,so that the angle between the tangent to the anchor and the seabed is not satisfied when the whole system is balanced. More than 16°,the inclination angle of the iron drum does not exceed 5°.