Research Papers: Polar and Arctic Engineering

A Modified Matlock–Duffing Model for Two-Dimensional Ice-Induced Vibrations of Offshore Structures With Geometric Nonlinearities

[+] Author and Article Information
Hugh McQueen

Department of Naval Architecture,
Ocean and Marine Engineering,
University of Strathclyde,
Glasgow G4 0LZ, UK

Narakorn Srinil

Department of Naval Architecture,
Ocean and Marine Engineering,
University of Strathclyde,
Glasgow G4 0LZ, UK

1Corresponding author.

2Present address: School of Marine Science & Technology, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received June 15, 2015; final manuscript received October 22, 2015; published online November 19, 2015. Assoc. Editor: Søren Ehlers.

J. Offshore Mech. Arct. Eng 138(1), 011501 (Nov 19, 2015) (9 pages) Paper No: OMAE-15-1046; doi: 10.1115/1.4031927 History: Received June 15, 2015; Revised October 22, 2015

Oil and gas exploration and production have been expanding in Arctic waters. However, numerical models for predicting the ice-induced vibrations (IIV) of offshore structures are still lacking in the literature. This study aims to develop a mathematical reduced-order model for predicting the two-dimensional IIV of offshore structures with geometric coupling and nonlinearities. A cylindrical structure subject to a moving uniform ice sheet is analyzed using the well-known Matlock model, which, in the present study, is extended and modified to account for a new empirical nonlinear stress–strain rate relationship determining the maximum compressive stress (MCS) of the ice. The model is further developed through the incorporation of ice temperature, brine content, air volume, grain size, ice thickness, and ice wedge angle effects on the ice compressive strength. These allow the effect of multiple ice properties on the ice–structure interaction to be investigated. A further advancement is the inclusion of an equation allowing the length of failed ice at a point of failure to vary with time. A mixture of existing equations and newly proposed empirical relationships is used. Structural geometric nonlinearities are incorporated into the numerical model through the use of Duffing oscillators, a technique previously proposed in vortex-induced vibration studies. The model is validated against results from the literature and provides new insights into IIV responses including the quasi-static, randomlike chaotic, and locked-in motions, depending on the ice velocity and system nonlinearities. This numerical Matlock–Duffing model shows a potential to be used in future IIV analysis of Arctic cylindrical structures, particularly fixed offshore structures, such as lighthouses, gravity bases, and wind turbine monopiles.

Copyright © 2016 by ASME
Topics: Ice , Stress
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Grahic Jump Location
Fig. 1

A schematic model of IIV

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Fig. 2

Comparison of new stress–strain rate formulae (dashed line) versus (a) Withalm and Hoffman [8] relationship and (b) experimental results collated by Kim and Keune [12]

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Fig. 5

(a) Maximum, RMS, and mean stress versus ice temperature, (b) maximum, RMS, and mean stress versus salinity, (c) maximum, RMS, and mean stress versus air volume, (d) compressive stress versus temperature [16], (e) compressive stress versus salinity [13], and (f) compressive stress versus air volume [13]

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Fig. 4

Displacement time histories: (a) U = 0.127 m/s and (b)U = 1.27 m/s

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Fig. 8

X–Y displacement for θ = 45 deg: (a) U = 0.064 m/s, (b) U = 0.25 m/s, and (c) U = 0.635 m/s; X (bottom line), Y (middle line), and in-line (top line) displacement for (d) U = 0.064 m/s, (e) U = 0.25 m/s, and (f) U = 0.635 m/s

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Fig. 3

(a) Compressive stress versus grain size for varying strain rates [19], (b) new compressive stress versus grain size formulae in Table 2 for varying strain rates, and (c) failed ice length histogram (U = 0.5 m/s)

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Fig. 6

Ice load time history comparison with field data (Molikpaq Event 5, Ref. [23])

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Fig. 7

(a) X–Y displacement trajectories for different asymmetric nonlinearities (U = 0.127 m/s and θ = 45 deg) and (b) X–Y displacement trajectories for θ = 30 deg, 45 deg, and 60 deg (U = 0.25 m/s, αx=αy  = 1.05, and βx=βy  = 0.35)

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Fig. 9

In-line force time histories for (a) U = 0.064 m/s, (b) U = 0.25 m/s, and (c) U = 0.635 m/s, phase-plane plots at U = 0.25 m/s for (d) X motion, (e) Y motion, and (f) zoomed-in view of Fig. 8(f) between 34 and 35 s




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