English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Risers are pipes that convey fluids from the seabed up to the floating platforms and vice-versa. Many configurations and materials are used, but only steel catenary risers (SCR) are studied in this work. Risers are extremely slender structures, and for this reason, most of the suspended part has cable behavior. Only in two regions the bending stiffness is important: at the hang-off and at the touch-down zone (TDZ), which is the most complex region for analysis because of the unilateral contact with the seabed. Due to several dynamic loads that the riser is subjected to, great curvature variations occur at the TDZ, apart from impacts and friction with the soil, which can reduce the life time of the structure or even jeopardize its integrity. For these reasons, this work aims at the development of an analytical methodology for the construction of a reduced-order model (ROM) able to analyze the nonlinear dynamic behavior of the TDZ of a SCR. As at the TDZ the bending stiffness prevails over the geometric stiffness, the riser is modeled as a semi-infinite beam, having a suspended part and another one resting on the elastic soil with unilateral contact. At the end of the suspended part, vertical displacements and dynamic tensions are imposed, that cause the TDP’s position to vary with time. It is, therefore, a problem with moving boundary conditions. The methodology adopted for solving this problem was to tranform it into a problem with fixed boundary conditions via a variable transformation. However, a “price is paid” for such a transformation, and strong nonlinearities appear in the differential equation of motion, making it extremely complex to solve analytically. For the simple bending problem, nonlinear vibration modes are obtained via the method of multiple scales. In possession of these modes, the nonlinear Galerkin method is used to project the complete equation into a chosen mode, transforming the continuum model into a reduced-order model (ROM) with only one degree of freedom whose modal generalized coordinate is the horizontal displacement of the TDP. After obtaining the ROM, it is noticed that there are coefficients that vary with time, as in the classic Mathieu equation, indicating the possibility of parametric resonance. In this kind of resonance, among other possibilities, the excitation frequency may be twice the natural frequency – it is the so-called principal parametric resonance. The ROM’s equation is integrated numerically and the responses are compared to those given by finite-element models studied with the help of commercial softwares, like Abaqus and Orcaflex. Finally, the potentialities and limitations of the ROM are discussed. One of the advantages is the possibility of processing several cases easily, changing the parameters that affect the responses. With this response mapping, it is possible to estimate the post-critical steady-state amplitudes that take place.

Modelagem dinâmica da zona de contato entre riser e fundo do mar sob ação de deslocamento e tração impostos.