Analytical Study of Nonlinear Vibrations of Marine Risers by Newton Harmonic Balance Method

Abstract

In this paper, the nonlinear motions of marine risers are studied using the Newton's Harmonic Balance Method (NHBM). The nonlinear vibrational equations of the marine risers were obtained in the present study using the Hamilton principle and the Euler–Bernoulli beam theory. The Galerkin's decomposition technique is used to convert the partial differential governing equation (PDE) of the riser vibrations to the ordinary differential equation (ODE). By using the NHBM method, an analytical formulation has been obtained to express the natural nonlinear frequency of the riser. The effect of design parameters such as riser length and initial static displacement of high support has been investigated on riser frequency, which shows acceptable accuracy after comparing the results with previous research. The results show that fluid damping coefficient has a great effect on system instability and reducing this coefficient increases the stability range of the system. Examining the effect of nonlinear parameters shows that the effect of these parameters is greater in large amplitude of motion.