Dynamic Modeling of Towed Cable System Using the Nodal Position Finite Element and Symplectic Integration

The cable of towed underwater system have a character of low tension, in order to overcome this singular problem during numerical calculation, the bending stiffness is included in the bar model, or using the beam model. however, we choose an alternative method called nodal position finite element method, it is different from the traditional finite element method, this alternative method is formulated in term of element nodal position that different with the nodal displacement used in traditional finite element. The model equation is derived from the principle of virtual work, consideration of the hydrodynamic drag force, gravity force, buoyancy and internal damping model. The energy conservative time integrator is preferred for the long term simulation, so we build up a simulation program that using the nodal position finite element method and symplectic leapfrog time integrator for the dynamic analysis of the towed body system. Firstly, the robustness of the proposed time integrator is verified by the elastic spring pendulum, and compared with the traditional frequently used time integrators such as fourth-order Runge-Kutta method and Newmark method, the results show that the proposed approach is accurate and preserves the system energy over long term simulation, then the proposed time integrator is applied to the dynamic modeling of the elastic cable towed system, the well agreement with Sea trail experiment date demonstrates that the simulation program is robust and accurate.