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TECHNICAL PAPERS

# Riser-Soil Interaction: Local Dynamics at TDP and a Discussion on the Eigenvalue and the VIV Problems

[+] Author and Article Information
Celso P. Pesce

Fluid-Structure Interaction and Offshore Mechanics Laboratory, Department of Mechanical Engineering, Escola Politécnica, University of São Paulo, São Paulo 05508-900, Brazilceppesce@usp.br

Clóvis de A. Martins

Fluid-Structure Interaction and Offshore Mechanics Laboratory, Department of Mechanical Engineering, Escola Politécnica, University of São Paulo, São Paulo 05508-900, Brazil and NDF—Nucleus for Dynamics and Fluids, Av. Prof. Mello Moraes 2231, São Paulo, SP 05508-900, Brazil

Lauro M. da Silveira

NDF—Nucleus for Dynamics and Fluids, Av. Prof. Mello Moraes 2231, São Paulo, SP 05508-900, Brazil

If compared to the dynamics of the supported part.

For dynamic compression, see (15-16).

$ηI$ indicates derivative with respect to the local coordinate $ξ$.

ORCAFLEX®, version 8.6.

As shown in Aranha et al. (8), the nonlinear hydrodynamic damping along the riser length causes clockwise and anti-clockwise motions to provoke quite different responses in the dynamic curvature at TDP.

See, e.g., Burridge et al. (17) for the treatment of a similar problem.

Triantafyllou uses the terms “slowly” and “fast” varying in space.

See, also, (19).

Though relatively poor, this estimate is generally in the safe side, as dynamic tension usually reduces dynamic curvature.

Actually, the transverse current makes the elastica to depart from the vertical plane.

In fact, the reduced velocity takes the value $Vr25=2πU∕Ω25D≅5.3$.

J. Offshore Mech. Arct. Eng 128(1), 39-55 (Aug 31, 2005) (17 pages) doi:10.1115/1.2151205 History: Received October 18, 2004; Revised August 31, 2005

## Abstract

The eigenvalue problem of risers is of utmost importance, particularly if vortex-induced vibration (VIV) is concerned. Design procedures rely on the determination of eigenvalues and eigenmodes. Natural frequencies are not too sensitive to the proper consideration of boundary condition, within a certain extent where dynamics at the touchdown area (TDA) may be modeled as dominated by the dynamics of the suspended part. However, eigenmodes may be strongly affected in this region because, strictly speaking, this is a nonlinear one-side (contact-type) boundary condition. Actually, we shall consider a nonlinear eigenvalue problem. Locally, at TDA, riser flexural rigidity and soil interaction play important roles and may affect the dynamic curvature. Extending and merging former analytical solutions on touchdown point (TDP) dynamics and on the eigenvalue problem, obtained through asymptotic and perturbation methods, the present work critically address soil and bending stiffness effects a little further. As far as linear soil stiffness and planar dynamics hypotheses may be considered valid, it is shown that penetration in the soil is small and that its effect does not change significantly the bending loading that is mainly caused by the cyclic excursion of the TDP and corresponding dynamic tension. A comparison of the analytical results with a full nonlinear time-domain simulation shows a remarkable agreement for a typical steel catenary riser. The WKB approximation for the eigenvalue problem gives good estimates for TDP excursion. As the dynamic tension caused solely by VIV is very small, the merged analytical solution may be used as a first estimate of the curvature variation at TDP in the cases of current perpendicular to the “riser plane.”

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## Figures

Figure 1

Two-dimensional catenary riser problem. Displacements exaggerated

Figure 2

Normalized elastic curve, K=10. Snapshots for t∕T=0,0.1,0.2,0.3,0.4,0.5; T=2πω−1. a0=1, β0=0.2.

Figure 3

Normalized angle, K=10. Snapshots for t∕T=0,0.1,0.2,0.3,0.4,0.5; T=2πω−1. a0=1, β0=0.2.

Figure 4

Normalized curvature, K=10. Snapshots for t∕T=0,0.1,0.2,0.3,0.4,0.5; T=2πω−1. a0=1, β0=0.2.

Figure 5

Normalized shear force, K=10. Snapshots for t∕T=0,0.1,0.2,0.3,0.4,0.5; T=2πω−1. a0=1, β0=0.2.

Figure 6

Normalized TDP excursion and dynamic tension in time: a0=1, β0=0.2, K=10

Figure 7

Normalized curvature in time at various sections: x∕λ=−6,−5,…,5,6; a0=1; β0=0.2; K=10

Figure 8

Normalized TDP excursion and dynamic tension in time: a0=1, β0=0.7, K=10

Figure 9

Normalized curvature in time at various sections: x∕λ=−6,−5,…,5,6; a0=1; β0=0.7; K=10

Figure 10

Normalized elastic curve. K=10. Snapshots for t∕T=0,0.1,0.2,0.3,0.4,0.5; T=2πω−1. a0=1; β0=0.7.

Figure 11

Normalized curvature. K=10. Snapshots for t∕T=0,0.1,0.2,0.3,0.4,0.5; T=2πω−1. a0=1; β0=0.7.

Figure 12

Normalized curvature in time at various sections: x∕λ=−6,−5,…,5,6; a0=1; β0=0.2; K=10,000

Figure 13

Normalized elastic curve, K=10,000. Snapshots for t∕T=0,0.1,0.2,0.3,0.4,0.5; T=2πω−1. a0=1; β0=0.2.

Figure 14

Normalized curvature, K=10,000. Snapshots for t∕T=0,0.1,0.2,0.3,0.4,0.5; T=2πω−1. a0=1; β0=0.2.

Figure 15

Nonlinear numerical simulation. Normalized TDP excursion, x0(t)∕λ, of a typical SCR.

Figure 16

Nonlinear numerical simulation. Normalized dynamic tension, τ0(t)∕T0, at TDP of a typical SCR.

Figure 17

Curvature time histories at x∕λ=4.0, at the critical section. Analytical and numerical solutions, K=10.

Figure 18

Curvature time histories at x∕λ=−3, a section that rests on the soil cyclically. Analytical and numerical solutions, K=10.

Figure 19

Curvature time histories at x∕λ=−3. Analytical and numerical solutions, K=1000.

Figure 20

Normalized curvature. Minimum value: (a) along the length and (b) as a function of the soil rigidity parameter K.

Figure 21

WKB approximate solution compared to numerical results obtained by a standard finite element method. Free-hanging SCR. No current. θL=70deg. Assessing the extensibility effect.

Figure 22

Natural frequencies of a SCR. Assessing the extensibility effect. Numerical solution, with three different values of axial rigidity, compared to the WKB analytical approximation. No current; θL=70deg.

Figure 23

Normalized elastic curve, K=10. Snapshots for t∕T=0,0.1,0.2,0.3,0.4,0.5; T=2πω−1. a0=2.08; β0≈O(10−6).

Figure 24

Snapshots of the normalized curvature, K=10. a0=2.08; β0≈O(10−6).

Figure 25

Snapshots of the normalized shear force, K=10. a0=2.08; β0≈O(10−6).

Figure 26

Normalized curvature in time at various sections, x∕λ=−6,−5,…,5,6; a0=2.08; β0≈O(10−6); K=10

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