水下缆索运动建模与仿真分析方法

Dynamic Modeling and Simulation of Underwater Cable

摘要:

水下缆索运动建模过程中出现低应力松弛状态、大弯曲或扭转等形变等状态，必须精细划分空间离散微元与时域求解步长以描述缆索曲率变化，进而避免数值求解奇异，这种处理方法使得求解水下缆索运动响应效率极为低下，甚至可能出现数值积分过程中截断误差与舍入误差累加导致的计算错误，无法描述水下锚泊、拖曳等系统的真实状态。针对精确描述水下柔性缆索的弯曲、扭转等形变状态及其对运动系统数学模型的影响，采用三次样条插值方法构建水下缆索微元空间形态，对连续水下缆索进行非线性离散而非常用的线性化离散，通过Galerkin余量消除方法实现求解域内满足缆索微元空间运动方程要求，建立了包含弯矩、扭矩作用的水下缆索动态运动数学模型与求解方法。通过与理论数值计算数据及海上实验数据对比分析，验证了本模型的准确性，可为水下锚泊系留、水下拖曳等系统的工程应用提供一种高效设计方法。

Abstract:

To determine the motion response of underwater cable which appear the state of low-tension and large bending or torsional deformation, the spatial discrete elements and time-domain solution step must be massively divided to describe the change of curvature and then avoid numerical singularity, this common method makes calculate efficiency of mooring or towing system motion response extremely low even results in calculation error owing to truncation error and rounding error. Aiming at accurately describing the bending, torsion and other large deformation states of underwater flexible cable and its influence on mooring or towing system mathematical model, the cubic spline interpolation method is used to construct non-linear cable micro element instead of the linear element in lumped mass method, the Galerkin’s residual elimination method is used to calculate the micro element differential equations including bending moment and torque in solution domain. The accuracy of the mathematical model is verified by comparing with theoretical numerical calculation results and experimental data and will provide a theoretical principle for associated works.