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.”

1.
Patel
,
M. H.
, and
Seyed
,
F. B.
, 1995, “
Review of Flexible Riser Modelling and Analysis Techniques
,”
Eng. Struct.
0141-0296,
17
(
4
), pp.
293
304
.
2.
Pesce
,
C. P.
, and
Martins
,
C. A.
, 2005, “
Numerical Computation of Riser Dynamics
,”
Numerical Modelling in Fluid-Structure Interaction
,
Advances in Fluid Mechanics Series
,
S.
Chakrabarti
ed.,
WIT Press
,
Southampton, UK
, Chap. 7, pp.
253
309
.
3.
Giertsen
,
E.
,
Verley
,
R.
, and
Schroder
,
K.
, 2004, “
CARISIMA a Catenary Riser/Soil Interaction Model for Global Riser Analysis
,”
ASME 23rd International Conference on Offshore Mechanics and Arctic Engineering
,
Vancouver
, Canada, June 20–25, ASME Paper No. OMAE2004-51345.
4.
Leira
,
B. J.
,
Passano
,
E.
,
Karunakaran
,
D.
, and
Farnes
,
K-H.
, 2004, “
Analysis Guidelines and Application of a Riser-Soil Interaction Model Including Trench Effects
,”
ASME 23rd Int. Conference on Offshore Mechanics and Arctic Engineering
, June 20–25, Vancouver, ASME Paper No. OMAE2004-51527.
5.
Fontaine
,
E.
,
Nauroy
,
J. F.
,
Foray
,
P.
,
Roux
,
A.
, and
Gueveneux
,
H.
, 2004, “
Pipe-Soil Interaction in Soft Kaolinite: Vertical Stiffness and Damping
,”
14th International Offshore and Polar Engineering Conference
, Vol.
2
, pp.
517
524
.
6.
Triantafyllou
,
M. S.
,
Bliek
,
A.
, and
Shin
,
H.
, 1985, “
Dynamic Analysis as a Tool for Open Sea Mooring System Design
,”
Annual Meeting of The Society of Naval Architects and Marine Eng.
, New York.
7.
Irvine
,
M.
, 1992, “
Local Bending Stress in Cables
,”
Proc. of 2nd Int. Offshore and Polar Engineering Conference
,
San Francisco
, June 11–19,
ISOPE
,
Golden, CO
, Vol.
2
, pp.
342
345
.
8.
Aranha
,
J. A. P.
,
Martins
,
C. A.
, and
Pesce
,
C. P.
, 1997, “
Analytical Approximation for the Dynamic Bending Moment at the Touchdown Point of a Catenary Riser
,”
Int. J. Offshore Polar Eng.
1053-5381,
7
(
4
), pp.
293
300
.
9.
Pesce
,
C. P.
,
Aranha
,
J. A. P.
,
Martins
,
C. A.
,
Ricardo
,
O. G. S.
, and
Silva
,
S.
, 1998, “
Dynamic Curvature in Catenary Risers at the Touchdown Point: An Experimental Study and the Analytical Boundary Layer Solution
,”
Int. J. Offshore Polar Eng.
1053-5381,
8
(
4
), pp.
302
310
.
10.
Pesce
,
C. P.
,
Aranha
,
J. A. P.
, and
Martins
,
C. A.
, 1998, “
The Soil Rigidity Effect in the Touchdown Boundary Layer of a Catenary Riser: Static Problem
,”
8th Int. Offshore and Polar Engineering Conference
, Montreal, May 24–29, 1998, Vol.
II
, pp.
207
213
.
11.
Kevorkian
,
J.
, and
Cole
,
J. D.
, 1981,
Perturbation Methods in Applied Mathematics
,
Applied Mathematical Sciences Vol. 34
,
Springer-Verlag
,
New York
.
12.
Bender
,
C. M.
, and
Orszag
,
S. A.
, 1978,
Advanced Mathematical Methods for Scientists and Engineers
,
International Series in Pure and Applied Mathematics
,
McGraw-Hill
,
New York
.
13.
Triantafyllou
,
M. S.
, 1984, “
The Dynamics of Taut Inclined Cables
,”
Q. J. Mech. Appl. Math.
0033-5614,
37
(
3
), pp.
431
440
.
14.
Pesce
,
C. P.
,
Fujarra
,
A. L. C.
,
Simos
,
A. N.
, and
Tannuri
,
E. A.
, 1999, “
Analytical and Closed Form Solutions For Deep Water Riser-Like Eigenvalue Problem
,”
9th Int. Offshore and Polar Engineering Conference
, Brest, France, June 1–6, Vol.
II
, pp.
255
263
.
15.
Aranha
,
J. A. P.
,
Pinto
,
M. O.
, and
Silva
,
R. M. C.
, 2001, “
On the Dynamic Compression of Risers: An Analytic Expression for the Critical Load
,”
Appl. Ocean. Res.
0141-1187,
23
(
2
), pp.
83
91
.
16.
Ramos
Jr.,
R.
, and
Pesce
,
C. P.
, 2003, “
A Stability Analysis of Risers Subjected to Dynamic Compression Coupled With Twisting
,”
ASME J. Offshore Mech. Arct. Eng.
0892-7219,
125
, pp.
183
189
.
17.
Burridge
,
R.
,
Kappraff
,
J.
, and
Morshedi
,
C.
, 1982, “
The Sitar String: A Vibrating-String With a One-sided Inelastic Constraint
,”
SIAM J. Appl. Math.
0036-1399,
42
(
6
), pp.
1231
1251
.
18.
Whitham
,
G. B.
, 1974,
Linear and Non-linear Waves
,
Pure and Applied Mathematics
,
Wiley
,
New York
.
19.
Chucheepsakul
,
S.
, and
Huang
,
T.
, 1997, “
Effect of Axial Deformation on Natural Frequencies of Marine Risers
,”
7th Int. Offshore and Polar Engineering Conference
, Honolulu, May 25–30, Vol.
II
, pp.
31
136
.
20.
Williamson
,
C. H. K.
, and
Govardhan
,
R.
, 2004, “
Vortex-Induced Vibrations
,”
Annu. Rev. Fluid Mech.
0066-4189,
36
, pp.
313
455
.
21.
Aranha
,
J. A. P.
, and
Pinto
,
M. M. O.
, 2001, “
Dynamic Tension in Risers and Mooring Lines: An Algebraic Approximation for Harmonic Excitation
,”
Appl. Ocean. Res.
0141-1187,
23
(
2
), pp.
83
91
.
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