Analytical-numerical investigations on vortex-induced vibrations and parametric excitation phenomena in flexible cylinders in vertical and catenary configurations

Abstract

Slender structures found in offshore engineering present a rich dynamic behavior from the scientific point-of-view and, consequently, demand a complex analysis. Both linear and nonlinear phenomena coexist and, hence, the complete analysis of this dynamics is not a trivial task. This research project will focus on two particular phenomena, namely, parametric excitation problems and Vortex-Induced Vibrations (VIV). The parametric excitation problems arise from the temporal variation of the geometric stiffness of slender structures such as, for example, TLP risers and tendons. On the other hand, VIV is a particular class of flow-induced vibration, characterized by amplitudes of oscillation close to one diameter. It is planned to carry out an analytical-numerical investigation analysis of these two phenomena in two particular configurations of a flexible cylinder, namely vertical catenary ones. Particularly, Reduced-Order Models (ROMs) will be analyzed, allowing the use of analytical techniques of nonlinear dynamics. ROMs are a complimentary approach to higher-order models (such as those based on the finite element method) and focus on representing the dynamics by means of a low number of degrees-of-freedom. As a first activity, it is intended to determine nonlinear modes for the problems of vertical cylinders and catenary. Then, these nonlinear modes will be used as projection functions in the Galerkin's method, employed to obtain the systems of differential equations representative of the ROMs. Parametric excitation problems will be studied using the ROMs employing analytical solutions (when possible) and numerical integration of the ROMS. The results will be compared woth those obtained with a computational tool based on the finite element method. VIV phenomenon will involve cylinders with one and two degrees-of-freedom and the hydrodynamic loads will be modeled by nonlinear equations coupled to structural oscillators, following a phenomenological approach. Numerical integration and analytical studies will be carried. It is also planned an analytical-numerical correlation with experimental data available in the research group. As final results, it is planned to highlight some aspects such as, for example, knowledge gains from the use of nonlinear modes as projection functions in the Galerkin method, the effects of a multimodal approach on the problems studied here, and a deep experimental correlation. (AU)