Static and Dynamic Behavior of Highly Deformed Risers and Pipelines

[+] Author and Article Information
Sophia T. Santillan

Department of Mechanical Engineering, United States Naval Academy, Annapolis, MD 21402

Lawrence N. Virgin1

Department of Mechanical Engineering, Duke University, Durham, NC 27708l.virgin@duke.edu

Raymond H. Plaut

Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0105rplaut@vt.edu


Corresponding author.

J. Offshore Mech. Arct. Eng 132(2), 021401 (Mar 01, 2010) (6 pages) doi:10.1115/1.4000555 History: Received July 02, 2007; Revised May 15, 2008; Published March 01, 2010; Online March 01, 2010

This paper models flexible risers and pipelines as slender elastica structures. The theoretical formulation leads to a type of nonlinear boundary value problem that can be solved numerically given appropriate boundary conditions. The offsetting effects of gravity and buoyancy are included in the analysis. These forces can provide considerable axial loading (as can thermal changes), and hence, stability (buckling) is a major concern. Initial studies are based on the planar problem. A free-vibration analysis is also conducted for small-amplitude oscillations about various deflected equilibrium configurations in terms of natural frequencies and corresponding mode shapes. Energy dissipation and fluid forces are key issues in the forced problem, especially when large deformations are involved. Free vibration information is a vital prerequisite in understanding the response of these types of structures in practice.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Steep–wave riser schematic

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Figure 2

Catenary configuration with d=1; ● denotes the numerical results using a finite difference method and the continuous line denotes the analytical solution

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Figure 3

Equilibrium configuration along with the bending moment m(s) resulting from the baseline values

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Figure 4

Static configurations with various buoyant segment lengths l2. The length l1 is chosen such that l1+0.5l2=0.5.

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Figure 5

Equilibrium riser configurations where the upper section length l3 is varied

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Figure 6

(a) Internal forces at the end points as a function of total length l (where only l3 is varied) and internal forces pe(s) and qe(s) for (b) l=1.6 and (c) l=2.3

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Figure 7

Static configurations for varying buoyancy coefficient values Bb

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Figure 8

The effect of a steady current with velocity V on the static configuration; fp values correspond to dimensional velocities of V=0 m/s, 1 m/s, and 2 m/s

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Figure 9

(a) Internal forces at the end points as a function of dimensional current velocity V and internal forces pe(s) and qe(s) along the riser length for (b) V=1 m/s and (c) V=2 m/s

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Figure 10

Mode shape corresponding to the first frequency of the riser (with baseline parameter values). The equilibrium configuration is given by the dotted line.

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Figure 11

Frequency Ω as a function of the buoyancy coefficient Bb

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Figure 12

Frequency as a function of buoyed segment length

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Figure 13

Frequency as a function of steady current velocity




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