Modeling the dynamic behavior of a coupled nonlinear flexible marine riser

Abstract

In this paper we analyze the dynamic aspect of a coupled system with a von Kármán type nonlinearity. First, using an approach of linear semigroup method combined with standard procedure for nonlinear evolution equations we obtain the global solution. Later, we use the energy perturbation method to establish the exponential decay of the solution as time goes to infinity. In the sequence, due to the non-linearity of the model we propose an effective numerical scheme using the finite element approximation for the variational formulation form corresponding. Then, using the Nakao Method, we show that the energy of the approximate solutions decays exponentially to zero, as time approaches to infinity and we show the rate convergence of the approximate model. Also, we present a numerical approximation to our system to obtain the numerical solution. The algorithms are based on the finite element method of the spatial variable and the implicit Newmark method to the discretized the temporal variable. We finish with some performed numerical experiments to highlight our theoretical results. It is worth noting that this type of approach has not been used in the literature.