Study of the parametric excitation phenomenon of a slender riser using finite element method and a reduced order model

Resumo

In the context of oil and gas (O&G) exploitation, risers are slender structures connecting the floating
unit to the seabed. These structures experience static and dynamic loads with potentially high nonlinearities. It is
relevant for O&G industry to understand the riser’s mechanical behavior to improve the structure life and predict
failures. In this sense, this work focuses on the analysis of the dynamical behavior of a vertical riser (represented
as a vertical beam) under harmonic excitation in the top, standing for the oscillation of a floating unit. Depending
on the structure’s mechanical properties and on the load frequency, the parametric excitation phenomenon can
take place, yielding large-amplitude lateral motion even for small vertical displacements. More specifically, the
focus is on the Mathieu’s instability regions, which occurs when the excitation frequency is an even multiple of
the structure natural frequency. In this work, we establish a simplified analytical approach using a reduced order
model (ROM), which considers an Euler-Bernoulli beam model undergoing small rotation. For this purpose, the
equations of motion are obtained using the extended Hamilton’s principle (EHP). By applying Galerkin’s method
using three sinusoidal shape functions and considering a time-spatial split, ROM’s non-dimensional final equations
can be obtained. Next, an in-house nonlinear FEM-based solver, called Giraffe (an acronym for “Generic Interface
Readily Accessible For Finite Element”) is presented and some comparative examples are performed using the
ROM and the Giraffe, observing their differences and similarities. These case studies were performed considering
the structure immersed in water and air, and the excitation frequency is varied to evaluate the first and the second
Mathieu’s instability region. The results presented good agreement in both models, with, in general, slightly larger
displacements for the ROM models.