A high accurate decoupling Hamiltonian absolute nodal coordinate formulation for dynamic analysis of towing cable with large deformation

Abstract

For the analysis of towing cable dynamics, the absolute nodal coordinate formulation in Hamiltonian formalism is an appropriate method which can describe the large displacement and rotation of the cable while reducing the accumulative error over long-term simulation. However, large deformations of cable element in such formulation can induce spurious elastic force, which can result in the distortion of the cable element. The magnitude of spurious elastic force increases with deformation amplitude, demonstrating a coupling between geometric nonlinearity and spurious elastic force that degrade the accuracy of dynamic solutions. This paper proposes a new Hamiltonian absolute nodal coordinate formulation for high accurate dynamic modeling of towing cables with large deformation. A stiffness matrix reevaluation enables decoupling modeling of deformation and elastic forces. Hamiltonian canonical equations and symplectic difference algorithm are derived for numerical calculation. The accuracy and efficiency of the proposed method are validated by a free swing flexible cable, a three-dimensional towing system with lumped mass, a rubber cable towing experiment and a submerged pendulum experiment. The proposed method exhibits higher accuracy and efficiency compared with the existing Hamiltonian absolute nodal coordinate formulation.