弯扭联合作用下的拖缆运动建模与分析

Dynamic Modeling and Analysis of Towed Low-Tension Cable with Bending and Torsion Effect

为解决水下低应力拖缆在弯扭联合作用下的运动建模问题,根据集中质量法基本原理,建立了一个四自由度(3个平动自由度和1个轴向转动自由度)运动数学模型,并采用数值仿真方法分析了弯扭矩对其运动的影响.借鉴材料力学概念给出了具体的三维弯矩、扭矩、剪力等的确定方法;同时,为解耦拖缆平动和转动之间的耦合关系,引入零扭矩转角来考虑平动的影响以确定缆上实际扭矩;在此基础上计入拖缆浮力、重力、流体阻力、张力及弯扭耦合,以形成一个完整的运动模型.最后给出了3个仿真算例,计算结果同实际弯扭影响运动规律一致,说明该模型是合理、有效的;同时计算结果还给出了一些有意义的运动规律.

A mathematical scheme was proposed and derived to study the dynamics of towed low tension cable with both bending and torsion moment.According to the principle of the classic lumped mass method,a 4-DOF（three degrees of translational motion and one degree of rotate motion） mathematical model was formulated,which is employed to analyze the effect of bending and torsion moment on cable.When modeling,the methods were given to determine the three dimensional bending moment,torsion moment and shear force,while a new variable,zero-torsion moment angle,was introduced to eliminate the effect of cable＇s translational motion on torsion moment and finally get the actual torsion moment,then taking the cable＇s buoyancy,weight,drag and tension into consideration so as to result in the whole mathematical model.Three simulation cases were presented subsequently,the results show good agreement with actual dynamic characters of bending and torsion moment＇s effect,which thus validates the proposed mathematical scheme;these results also turn out some valuable conclusions.