The vortex-induced oscillation of TLP tether is investigated in the vicinity of lock-in condition. The vortex shedding is caused purely due to current, which may vary across the depth of the sea. The vibration of TLP is modeled as a SDOF problem by assuming that the first mode response of the tether dominates the motion. Nonlinearity in the equation of motion is produced due to the relative velocity squared drag force. In order to trace different branches of the response curve and investigate different instability phenomena that may exist, an arc-length continuation technique along with the incremental harmonic balance method (IHBC) is employed. A procedure for treating the nonlinear term using distribution theory is presented so that the equation of motion is transformed to a form amenable to the application of IHBC. The stability of the solution is investigated by the Floquet theory using Hsu’s scheme.
Issue Section:
Safety and Reliability
1.
Natvig
, B. J.
, and Pendered
, J. W.
, 1977, “Nonlinear Motion Response of Floating Structures to Wave Excitation
,” Proceedings of Ninth Annual Offshore Technology Conference
(OTC-2796), p. 1
.2.
Johnson
, C. P.
, Mekha
, B. B.
, and Roesset
, J. M.
, 1993, “Simplified Modeling for the Nonlinear Response of Tension Leg Platforms in Deep Water
,” Proceedings of the Third International Offshore and Polar Engineering Conference
, Singapore
, pp. 326
–333
.3.
Dong
, Y.
, and Lou
, J. Y. K.
, 1991, “Vortex-induced Nonlinear Oscillation of Tension Leg Platform Tethers
,” Ocean Eng.
0029-8018, 18
(5
), pp. 451
–464
.4.
Friedmann
, P.
, Hammond
, C. E.
, and Woo
, T.-H.
, 1977, “Efficient Numerical Treatment of Periodic Systems With Application to Stability Problems
,” Int. J. Numer. Methods Eng.
0029-5981, 11
, pp. 1117
–1136
.5.
Chua
, L. O.
, and Ushida
, A.
, 1981, “Algorithms for Computing Almost Periodic Steady-State Response of Nonlinear Systems to Multiple Input Frequencies
,” IEEE Circuits Syst. Mag.
1531-636X, CAS-28
, pp. 953
–971
.6.
Burton
, T. D.
, 1982, “Nonlinear Oscillator Limit Cycle Analysis Using a Finite Transformation Approach
,” Int. J. Non-Linear Mech.
0020-7462, 17
, pp. 7
–19
.7.
Nayfeh
, A. H.
, and Balachandran
, B.
, 1995, Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods
, Wiley
, New York
.8.
Sinha
, S. C.
, Bibb
, J. S.
, and Pandiyan
, R.
, 1996, “Liapunov–Floquet Transformation: Computation and Applications to Periodic Systems
,” ASME J. Vibr. Acoust.
0739-3717, 118
, pp. 209
—219
.9.
Bishop
, S. R.
, and Virgin
, L. N.
, 1988, “The Onset of Chaotic Motions of a Moored Semi-submersible
,” ASME J. Offshore Mech. Arct. Eng.
0892-7219, 110
, pp. 205
–209
.10.
Gottlieb
, O.
, and Yim
, S. C. S.
, 1992, “Nonlinear Oscillations, Bifurcations and Chaos in a Multi-Point Mooring System with a Geometric Nonlinearity
,” Appl. Ocean. Res.
0141-1187, 14
, pp. 241
–257
.11.
Lau
, S. L.
, Cheung
, Y. K.
, and Wu
, S. Y.
, 1982, “A Variable Parameter Incrementation Method for Dynamic Instability of Linear and Nonlinear Elastic Systems
,” ASME J. Appl. Mech.
0021-8936, 49
, pp. 849
–853
.12.
Pierre
, C.
, Ferri
, A. A.
, and Dowell
, E. H.
, 1985, “Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method
,” ASME J. Appl. Mech.
0021-8936, 52
, pp. 958
–964
.13.
Lau
, S. L.
, and Yuen
, S. W.
, 1993, “Solution Diagram of Nonlinear Dynamic Systems by the IHB Method
,” J. Sound Vib.
0022-460X, 167
(2
), pp. 303
–316
.14.
Leung
, A. Y. T.
, and Chui
, S. K.
, 1995, “Nonlinear Vibration of Coupled Duffing Oscillators by an Improved Incremental Harmonic Balance Method
,” J. Sound Vib.
0022-460X, 181
(4
), pp. 619
–633
.15.
Raghothama
, A.
, and Narayanan
, S.
, 2000, “Bifurcations and Chaos of an Articulated Loading Platform With Piecewise Nonlinear Stiffness Using the Incremental Harmonic Balance Method
,” Ocean Eng.
0029-8018, 27
, pp. 1087
–1107
.16.
Xu
, L.
, Lu
, M. W.
, and Cao
, Q.
, 2002, “Nonlinear Vibrations of Dynamical Systems With a General Form of Piecewise-Linear Viscous Damping by Incremental Harmonic Balance Method
,” Phys. Lett. A
0375-9601, 301
, pp. 65
–73
.17.
Thompson
, J. M. T.
, Bokian
, A. R.
, and Ghaffari
, R.
, 1984, “Subharmonic and Chaotic Motions of Compliant Offshore Structure and Articulated Mooring Towers
,” ASME J. Energy Resour. Technol.
0195-0738, 106
, pp. 191
–198
.18.
Sharma
, S. D.
, Jiang
, T.
, and Schellin
, T. E.
, 1988, “Dynamic Instability and Chaotic Motions of a Single-Point Moored Tanker
,” 17th Symposium on Naval Hydrodynamics
, The Hague
, pp. 543
–563
.19.
Dong
, Y.
, Xie
, G.
, and Lou
, J. Y. K.
, 1992, “Stability of Vortex-Induced Oscillations of Tension Leg Platform Tethers
,” Ocean Eng.
0029-8018, 19
(6
), pp. 555
–571
.20.
Seydel
, R.
, 1995, Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos
, Springer-Verlag
, New York
.Copyright © 2009
by American Society of Mechanical Engineers
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