Nonlinear free vibrations of marine risers/pipes transporting fluid

An investigation emphasizing on nonlinear free vibrations of marine risers/pipes to determine the nonlinear natural frequencies and their corresponding mode shapes is presented in this paper. Based on the virtual work-energy functional of marine risers/pipes, the structural model developed consists of the strain energy due to axial deformation, strain energy due to bending, virtual works due to effective tension and external forces, and also the kinetic energy due to both the riser and the internal fluid motions. Nonlinear equations of motion coupled in axial and transverse displacements are derived through the Hamilton's principle. To analyze the nonlinear free vibrational behaviors, the system formulation has been reformed to the eigenvalue problem. The nonlinear fundamental frequencies and the corresponding numerically exact mode shapes are determined by the modified direct iteration technique incorporating with the inverse iteration. The significant influences of the marine riser's parameters studied on its nonlinear phenomena are then illustrated here first. Those parameters demonstrate the nonlinear effects due to the flexural rigidity, top tensions, internal flow velocities, and static offsets.