So, to analyze the problem of a catenary riser subjected to parametric excitation, three models were considered. In the riser problem, the time variance of the stiffness is attributed to the axial force variation due to the riser vibration. Parametric excitation can be better understood considering the so-called Mathieu equation: In this case, one may have, apart from the 1:1 resonance, other ratios, like 2:1 where the excitation frequency is twice of the natural frequency. Unlike the classical resonance, where the excitation frequency is equal or close to a natural frequency of the structure, the parametric resonance occurs when some parameter of the equation of motion varies periodically with time, for instance, the stiffness. In this nonlinear scenario, interesting dynamic phenomena may appear, like parametric resonances, which is the main subject of study in this paper. One may have combination of platform movements, waves, internal flow, currents acting in different directions, levels and intensities, which in turn trigger VIV's (vortex induced vibrations). The nature and amount of dynamic loads that the riser is subjected to makes the problem even more complex. Other important geometric nonlinearities are the unilateral contact and friction between riser and soil, and the hydrodynamic interaction between structure and fluid that generates nonlinear damping and lift forces. Only in two regions the bending behavior is relevant, at the hang-off and at the touch-down zones. Due to its slenderness, most part of the riser has cable behavior, where the equilibrium configuration depends on the tension and the tension depends on the equilibrium configuration. Several sources of nonlinearities are present in a catenary riser analysis, making it a very complex system to study. There are different configurations of risers, among them vertical, catenary, lazy-wave and steep-wave risers, but only catenary risers are studied in this paper. Risers are extremely slender pipes that convey oil and gas from the seabed up to the offshore platforms. Keywords: Finite-element modeling, reduced-order modeling, riser, parametric instability, nonlinear dynamics, unilateral contact. The aim of this study is to discuss the feasibility, potentialities and limitations of the analytical model in confrontation with the specialist and the generalist softwares for the analysis of risers, under conditions of parametric excitation and unilateral contact at the seabed. The third model is an analytical reduced-order model that represents only the touch-down zone.
Two are finite-element models, one studied with Orcaflex, an offshore marine system analysis software, and another one with Abaqus, a generalist structural analysis software.
In this work, three catenary riser models subjected to harmonic oscillations are studied. MazzilliĮscola Politécnica da Universidade de São Paulo, Av. An analysis of parametric instability of risersĪuthor Fernando Y.
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