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Journal of Offshore Mechanics and Arctic Engineering | Volume 133 | Issue 4 | Polar and Arctic Science and Technology
Polar and Arctic Science and Technology

Modal Analysis of the Ice-Structure Interaction Problem

[+] Author and Article Information
Michael A. Venturella

 United States Coast Guard, 2100 Second Street, SW Washington, DC 20593

Mayuresh J. Patil, Leigh S. McCue

Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

J. Offshore Mech. Arct. Eng 133(4), 041501 (Apr 11, 2011) (18 pages) doi:10.1115/1.4003388 History: Received August 12, 2008; Revised October 21, 2010; Published April 11, 2011; Online April 11, 2011
Article
References
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Citing Articles

In this paper the authors present a multimode ice-structure interaction model based on the single degree of freedom ice-structure interaction model initially proposed by Matlock (1969, “A Model for the Prediction of Ice-Structure Interaction,” Proceedings of the First Offshore Technology Conference, Houston, TX, Vol. 1, pp. 687–694, Paper No. OTC 1066; 1971, “Analytical Model for Ice Structure Interaction,” ASCE Journal of the Engineering Mechanics Division, EM4, pp. 1083–1092). The model created by Matlock assumed that the primary response of the structure would be in its fundamental mode of vibration. In order to glean a greater physical understanding of the ice-structure interaction phenomena, it was critical that this study set out to develop a multimode forced response for the pier when a moving ice floe makes contact at a specific vertical pier location. Modal analysis is used in this study, in which the response of each mode is superposed to find the complete modal response of the entire length of a pier subject to incremental ice loading. This incremental ice loading includes ice fracture points as well as loss of contact between ice and structure. In the work of Matlock , the physical system is a bottom supported pier modeled as a cantilever beam. Realistic conditions such as ice accumulation on the pier modeled as a point mass and uncertainties in the ice characteristics are introduced in order to provide a stochastic response. The impact of number of modes in modeling is studied as well as dynamics due to fluctuations of ice impact height as a result of typical tidal fluctuations. A Poincaré based analysis following on the research of Karr (1992, “Nonlinear Dynamic Response of a Simple Ice-Structure Interaction Model,” Proceedings of the 11th International Conference of Offshore Mechanics and Arctic Engineering, Vol. 4, pp. 231–237) is employed to identify any periodic behavior of the low and high velocity ice system responses. Recurrence plotting is also utilized to further define any existing structure of the ice-structure interaction time series for low and high speed ice floes. While the Matlock model on which this research is based is admittedly simplistic, the intention of this work is to provide a foundation for future work using time series analysis and modal analysis on more sophisticated models coupling multiple piers and connecting structure for a comprehensive ice-wind-structural dynamics model.
Copyright © 2011 by American Society of Mechanical Engineers
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References

1
Matlock, H., Dawkins, W. P., and Panak, J. J., 1969, “A Model for the Prediction of Ice-Structure Interaction,” Proceedings of the First Offshore Technology Conference , Houston, TX, Vol. 1 , pp. 687–694, Paper No. OTC 1066.
2
Matlock, H., Dawkins, W. P., and Panak, J. J., 1971, “Analytical Model for Ice Structure Interaction,” ASCE Journal of the Engineering Mechanics Division, EM4 , pp. 1083–1092.
3
Blenkarn, K. A., 1970, “Measurement and Analysis of Ice Forces on Cook Inlet Structures,” Offshore Technology Conference , Paper No. OTC 1261.
4
Karr, D. G., Troesch, A. W., and Wingate, W. C., 1992, “Nonlinear Dynamic Response of a Simple Ice-Structure Interaction Model,” Proceedings of the 11th International Conference of Offshore Mechanics and Arctic Engineering , Vol. 4 , pp. 231–237.
5
Timco, G. W., and Jordaan, I. J., 1987, “Time-Series Variations in Ice Crushing,” Ninth International Conference Port and Ocean Engineering and Arctic Conditions , Fairbanks, AK, Vol. 1 , pp. 13–20.
6
Eranti, E. M., and Lee, G. C., 1986, "Cold Region Structural Engineering", McGraw-Hill, New York.
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Michel, B., and Toussaint, N., 1976, “Mechanism and Theory of Indentation of Ice Plates,” J. Glaciol., 18 (81), pp. 285–300.
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Frederking, R. N., 1977, “Plain Strain Compressive Strength of Columnar-Grained and Granular-Snow Ice,” J. Glaciol., 18 (89), pp. 506–516.
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Peyton, H. R., 1966, “Sea Ice Strength,” Office of Naval Research, Geophysical Institute, University of Alaska, Final Report No. UAG-R-182.
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Hegger, R., Kantz, H., and Schreiber, T., 1999, “Practical implementation of Nonlinear Time Series Methods: The TISEAN Package,” Chaos, 9 (2), pp. 413–435.  [CrossRef]
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Webber, C. L., 1996, http://homepages.luc.edu/~cwebber/.
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Venturella, M. A., 2008, "Modal Analysis of the Ice-Structure Interaction Problem", Virginia Polytechnic Institute and State University, Blacksburg, VA.
13
Heinonen, J., 2004, “Constitutive Modeling of Ice Rubble in First-Year Ridge Keel,” Ph.D. thesis, Helsinki University of Technology, Espoo, Finland, VTT Technical Research Center of Finland Publication No. 536.
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Huang, Y., Shi, Q., and Song, A., 2007, “Model Test Study of the Interaction Between Ice and a Compliant Vertical Narrow Structure,” Cold Regions Sci. Technol., 49 , pp. 151–160.  [CrossRef]
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Izumiyama, K., Irani, M. B., and Timco, G. W., 1994, “Influence of a Rubble Field in Front of a Conical Structure,” Proceedings of the Fourth International Offshore and Polar Engineering Conference (ISOPE) , Osaka, Japan, Vol. II , pp. 553–558.
16
Karna, T., 2001, “Simplified Modeling of Ice-Induced Vibrations of Offshore Structures,” Proceedings of the 16th International Symposium on Okhotsk Sea and Sea Ice , Feb., pp. 114–122.
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Kärnä, T., Kamesaki, K., and Tsukuda, H., 1999, “A Numerical Model for Dynamic Ice-Structure Interaction,” Comput. Struct., 72 , pp. 645–658.  [CrossRef]
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Shkhinek, K., Loset, S., and Karna, T., 2003, “Global Ice Load Dependency on Structure Width and Ice Thickness,” Proceedings of the 17th International Conference on Port and Ocean Engineering Under Arctic Conditions POAC’03 , Trondheim, Norway, Jun. 16–19.
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Timco, G. W., 1984, “Ice Forces on Structures: Physical Modeling Techniques,” "Second IAHR State-of-the-Art Report on Ice Forces on Structures", "Proceedings of the IAHR Symposium on Ice", Hamburg, Germany, M.Maattanen, ed., Chap. 2, Vol. IV .
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Squire, V. A., 2007, “Of Ocean Waves and Sea-Ice Revisited,” Cold Regions Sci. Technol., 49 , pp. 110–133.  [CrossRef]
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Engelbrektson, A., and Janson, J. E., 1985, “Field Observations of Ice Action on Concrete Structures in the Baltic Sea,” Concrete International , Aug.
23
Cornett, A. M., and Timco, G. W., 1998, “Ice Loads on an Elastic Model of the Molikpaq,” Appl. Ocean. Res., 20 , pp. 105–118.  [CrossRef]
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Izumiyama, K., and Uto, S., 1997, “Ice Loading on a Compliant Indentor,” "Proceedings of the 1997 Offshore Mechanics and Arctic Engineering Conference", Arctic/Polar Technology, Yokohama, Japan, Vol. IV .
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Kato, K., and Kumakura, Y., 1996, “First Year Ice Interactions on Molikpaq: Measurements and Experiments,” J. Mar. Sci. Technol., 1 , pp. 220–229.  [CrossRef]
26
Singh, S. K., Timco, G. W., Frederking, R. M. W., and Jordaan, L. J., 1990, “Tests of Ice Crushing on a Flexible Structure,” Proceedings of the Ninth Offshore Mechanics and Arctic Engineering Symposium , pp. 89–94.
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Sodhi, D. S., 1998, “Nonsimultaneous Crushing During Edge Indentation of Freshwater Ice Sheets,” Cold Regions Sci. Technol., 27 , pp. 179–195.  [CrossRef]
28
Timco, G. W., and Pratte, B. D., 1985, “The Force of a Moving Ice Cover on a Pair of Vertical Piles,” Proceedings of the Canadian Coastal Conference , Newfoundland, Canada, pp. 349–362.
29
Yue, Q., Bi, X., Sun, B., Zhang, T., and Chen, X., 1996, Full Scale Ice Force Measurement on JZ20-2 Platform,” IAHR Ice Symposium 1996 , Beijing, China, pp. 282–289.
30
Yue, Q., Zhang, X., Bi, X., and Shi, Z., 2001, Measurements and Analysis of Ice Induced Steady State Vibration,” Proceedings of the 16th International Conference on Port and Ocean Engineering Under Arctic Conditions, POAC 2001 , Ottawa, Canada.
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Bjerkas, M., Moslet, P. O., Jochmann, P., and Loset, S., 2003, “Global Ice Loads on the Lighthouse Norstromsgrund in the Winter 2001,” Proceedings of the 17th International Conference on Port and Ocean Engineering Under Arctic Conditions POAC’03 , Trondheim, Norway, Jun. 16–19.
32
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33
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34
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Figures

Grahic Jump Location
+Poincaré map–high velocity ice impact at 120 in. (3.048 m)
View Large  |  Save Figure  |  Download Slide (.ppt)
Poincaré map–high velocity ice impact at 120 in. (3.048 m)
Figure 9

Poincaré map–high velocity ice impact at 120 in. (3.048 m)

Grahic Jump Location
+Local recurrence plot (nondimensionalized, reduced neighborhood size)—high velocity ice impact at 192 in. (4.877 m)
View Large  |  Save Figure  |  Download Slide (.ppt)
Local recurrence plot (nondimensionalized, reduced neighborhood size)—high velocity ice impact at 192 in. (4.877 m)
Figure 15

Local recurrence plot (nondimensionalized, reduced neighborhood size)—high velocity ice impact at 192 in. (4.877 m)

Grahic Jump Location
+Gaussian force/pitch—impact at 120 in. (3.048 m) height (with point mass)
View Large  |  Save Figure  |  Download Slide (.ppt)
Gaussian force/pitch—impact at 120 in. (3.048 m) height (with point mass)
Figure 23

Gaussian force/pitch—impact at 120 in. (3.048 m) height (with point mass)

Grahic Jump Location
+Dynamic ice-structure interaction model reproduced with permission (Matlock , 1969, 1971)
View Large  |  Save Figure  |  Download Slide (.ppt)
Dynamic ice-structure interaction model reproduced with permission (Matlock , 1969, 1971)
Figure 1

Dynamic ice-structure interaction model reproduced with permission (Matlock , 1969, 1971)

Grahic Jump Location
+Twenty mode multilocation simulation—low velocity ice impact at 192 in. (4.877 m)
View Large  |  Save Figure  |  Download Slide (.ppt)
Twenty mode multilocation simulation—low velocity ice impact at 192 in. (4.877 m)
Figure 2

Twenty mode multilocation simulation—low velocity ice impact at 192 in. (4.877 m)

Grahic Jump Location
+Poincaré map—low velocity ice at 192 in. (4.877 m) impact height
View Large  |  Save Figure  |  Download Slide (.ppt)
Poincaré map—low velocity ice at 192 in. (4.877 m) impact height
Figure 3

Poincaré map—low velocity ice at 192 in. (4.877 m) impact height

Grahic Jump Location
+Poincaré map—high velocity ice impact at 192 in. (4.877 m)
View Large  |  Save Figure  |  Download Slide (.ppt)
Poincaré map—high velocity ice impact at 192 in. (4.877 m)
Figure 5

Poincaré map—high velocity ice impact at 192 in. (4.877 m)

Grahic Jump Location
+Ten mode multiple location—low velocity ice at 120 in. (3.048 m) impact height
View Large  |  Save Figure  |  Download Slide (.ppt)
Ten mode multiple location—low velocity ice at 120 in. (3.048 m) impact height
Figure 6

Ten mode multiple location—low velocity ice at 120 in. (3.048 m) impact height

Grahic Jump Location
+Poincaré map—low velocity ice at 160 in. (4.064 m) impact height
View Large  |  Save Figure  |  Download Slide (.ppt)
Poincaré map—low velocity ice at 160 in. (4.064 m) impact height
Figure 11

Poincaré map—low velocity ice at 160 in. (4.064 m) impact height

Grahic Jump Location
+Ten mode multiple location—high velocity ice at 160 in. (4.064 m) height
View Large  |  Save Figure  |  Download Slide (.ppt)
Ten mode multiple location—high velocity ice at 160 in. (4.064 m) height
Figure 12

Ten mode multiple location—high velocity ice at 160 in. (4.064 m) height

Grahic Jump Location
+Poincaré map overlaid on phase plane—high velocity ice impact at 160 in. (4.064 m)
View Large  |  Save Figure  |  Download Slide (.ppt)
Poincaré map overlaid on phase plane—high velocity ice impact at 160 in. (4.064 m)
Figure 13

Poincaré map overlaid on phase plane—high velocity ice impact at 160 in. (4.064 m)

Grahic Jump Location
+Local recurrence plot (nondimensionalized, reduced neighborhood size)—high velocity ice impact at 120 in. (3.048 m)
View Large  |  Save Figure  |  Download Slide (.ppt)
Local recurrence plot (nondimensionalized, reduced neighborhood size)—high velocity ice impact at 120 in. (3.048 m)
Figure 17

Local recurrence plot (nondimensionalized, reduced neighborhood size)—high velocity ice impact at 120 in. (3.048 m)

Grahic Jump Location
+Ten mode multiple location—high velocity ice at 120 in. (3.048 m) impact height
View Large  |  Save Figure  |  Download Slide (.ppt)
Ten mode multiple location—high velocity ice at 120 in. (3.048 m) impact height
Figure 8

Ten mode multiple location—high velocity ice at 120 in. (3.048 m) impact height

Grahic Jump Location
+Local recurrence plot (nondimensionalized)—low velocity ice impact at 192 in. (4.877 m)
View Large  |  Save Figure  |  Download Slide (.ppt)
Local recurrence plot (nondimensionalized)—low velocity ice impact at 192 in. (4.877 m)
Figure 14

Local recurrence plot (nondimensionalized)—low velocity ice impact at 192 in. (4.877 m)

Grahic Jump Location
+Ten mode multiple location—low velocity ice at 160 in. (4.064 m) height
View Large  |  Save Figure  |  Download Slide (.ppt)
Ten mode multiple location—low velocity ice at 160 in. (4.064 m) height
Figure 10

Ten mode multiple location—low velocity ice at 160 in. (4.064 m) height

Grahic Jump Location
+Local recurrence plot (nondimensionalized, last 3 s)—low velocity ice impact at 120 in. (3.048 m)
View Large  |  Save Figure  |  Download Slide (.ppt)
Local recurrence plot (nondimensionalized, last 3 s)—low velocity ice impact at 120 in. (3.048 m)
Figure 16

Local recurrence plot (nondimensionalized, last 3 s)—low velocity ice impact at 120 in. (3.048 m)

Grahic Jump Location
+Twenty mode multilocation simulation—high velocity ice impact at 192 in. (4.877 m)
View Large  |  Save Figure  |  Download Slide (.ppt)
Twenty mode multilocation simulation—high velocity ice impact at 192 in. (4.877 m)
Figure 4

Twenty mode multilocation simulation—high velocity ice impact at 192 in. (4.877 m)

Grahic Jump Location
+Poincaré map—low velocity ice at 120 in. (3.048 m) impact height
View Large  |  Save Figure  |  Download Slide (.ppt)
Poincaré map—low velocity ice at 120 in. (3.048 m) impact height
Figure 7

Poincaré map—low velocity ice at 120 in. (3.048 m) impact height

Grahic Jump Location
+Local recurrence plot (nondimensionalized, last 4 s)—low velocity ice impact at 160 in. (4.064 m)
View Large  |  Save Figure  |  Download Slide (.ppt)
Local recurrence plot (nondimensionalized, last 4 s)—low velocity ice impact at 160 in. (4.064 m)
Figure 18

Local recurrence plot (nondimensionalized, last 4 s)—low velocity ice impact at 160 in. (4.064 m)

Grahic Jump Location
+Local recurrence plot (nondimensionalized)—high velocity ice impact at 160 in. (4.064 m)
View Large  |  Save Figure  |  Download Slide (.ppt)
Local recurrence plot (nondimensionalized)—high velocity ice impact at 160 in. (4.064 m)
Figure 19

Local recurrence plot (nondimensionalized)—high velocity ice impact at 160 in. (4.064 m)

Grahic Jump Location
+Gaussian force/pitch—impact at 192 in. (4.877 m) height (with point mass)
View Large  |  Save Figure  |  Download Slide (.ppt)
Gaussian force/pitch—impact at 192 in. (4.877 m) height (with point mass)
Figure 20

Gaussian force/pitch—impact at 192 in. (4.877 m) height (with point mass)

Grahic Jump Location
+Gaussian force/pitch—impact at 192 in. (4.877 m) height (with point mass)
View Large  |  Save Figure  |  Download Slide (.ppt)
Gaussian force/pitch—impact at 192 in. (4.877 m) height (with point mass)
Figure 21

Gaussian force/pitch—impact at 192 in. (4.877 m) height (with point mass)

Grahic Jump Location
+Gaussian force/pitch—impact at 120 in. (3.048 m) height (with point mass)
View Large  |  Save Figure  |  Download Slide (.ppt)
Gaussian force/pitch—impact at 120 in. (3.048 m) height (with point mass)
Figure 22

Gaussian force/pitch—impact at 120 in. (3.048 m) height (with point mass)

Grahic Jump Location
+Gaussian force/pitch—impact at 160 in. (4.064 m) height (with point mass)
View Large  |  Save Figure  |  Download Slide (.ppt)
Gaussian force/pitch—impact at 160 in. (4.064 m) height (with point mass)
Figure 24

Gaussian force/pitch—impact at 160 in. (4.064 m) height (with point mass)

Grahic Jump Location
+Gaussian force/pitch—impact at 160 in. (4.064 m) height (with point mass)
View Large  |  Save Figure  |  Download Slide (.ppt)
Gaussian force/pitch—impact at 160 in. (4.064 m) height (with point mass)
Figure 25

Gaussian force/pitch—impact at 160 in. (4.064 m) height (with point mass)

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