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Research Papers: Structures and Safety Reliability

Wave Interaction With Floating Elastic Plate Based on the Timoshenko–Mindlin Plate Theory

[+] Author and Article Information
K. M. Praveen

Department of Applied Mechanics and Hydraulics,
National Institute of Technology Karnataka,
Surathkal, Mangalore 575025, India
e-mail: praveen.kodalingana@gmail.com

D. Karmakar

Department of Applied Mechanics and Hydraulics,
National Institute of Technology Karnataka,
Surathkal, Mangalore 575025, India
e-mail: dkarmakar@nitk.edu.in

C. Guedes Soares

Centre for Marine Technology and Ocean Engineering (CENTEC),
Instituto Superior Técnico, Universidade de Lisboa,
Av. Rovisco Pais, 1049-001 Lisboa, Portugal
e-mail: c.guedes.soares@centec.tecnico.ulisboa.pt

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the Journal of Offshore Mechanics and Arctic Engineering. Manuscript received May 28, 2018; final manuscript received May 10, 2019; published online June 5, 2019. Assoc. Editor: Hagbart S. Alsos.

J. Offshore Mech. Arct. Eng 142(1), 011601 (Jun 05, 2019) (15 pages) Paper No: OMAE-18-1064; doi: 10.1115/1.4043805 History: Received May 28, 2018; Accepted May 14, 2019

In the present study, the wave interaction with the very large floating structures (VLFSs) is analyzed considering the small amplitude wave theory. The VLFS is modeled as a 2D floating elastic plate with infinite width based on Timoshenko–Mindlin plate theory. The eigenfunction expansion method along with mode-coupling relation is used to analyze the hydroelastic behavior of VLFSs in finite water depth. The contour plots for the plate covered dispersion relation are presented to illustrate the complexity in the roots of the dispersion relation. The wave scattering behavior in the form of reflection and transmission coefficients are studied in detail. The hydroelastic performance of the elastic plate interacting with the ocean wave is analyzed for deflection, strain, bending moment, and shear force along the elastic plate. Further, the study is extended for shallow water approximation, and the results are compared for both Timoshenko–Mindlin plate theory and Kirchhoff’s plate theory. The significance and importance of rotary inertia and shear deformation in analyzing the hydroelastic characteristics of VLFSs are presented. The study will be helpful for scientists and engineers in the design and analysis of the VLFSs.

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References

Watanabe, E., Utsunomiya, T., and Wang, C. M., 2004, “Hydroelastic Analysis of Pontoon-Type VLFS: A Literature Survey,” Eng. Struct., 26(2), pp. 245–256. [CrossRef]
Kashiwagi, M., 2000, “Research on Hydroelastic Responses of VLFS: Recent Progress and Future Work,” Int. J. Offshore Polar Eng., 10(2), pp. 81–90.
Ohmatsu, S., 2005, “Overview: Research on Wave Loading and Responses of VLFS,” Mar. Struct.., 18(2), pp. 149–168. [CrossRef]
Chen, X. J., Moan, T., Fu, S., and Cui, W., 2006, “Second-Order Hydroelastic Analysis of a Floating Plate in Multidirectional Irregular Waves,” Int. J. Nonlin. Mech., 41(10), pp. 1206–1218. [CrossRef]
Squire, V. A., 2007, “Of Ocean Waves and Sea-Ice Revisited,” Cold Reg. Sci. Technol., 49(2), pp. 110–133. [CrossRef]
Squire, V. A., 2011, “Past, Present and Impendent Hydroelastic Challenges in the Polar and Subpolar Areas,” Philos. Trans. R. Soc. A, 369(1947), pp. 2813–2831. [CrossRef]
Pardo, M. L., Iglesias, G., and Carral, L., 2015, “A Review of Very Large Floating Structures (VLFS) for Coastal and Offshore Uses,” Ocean Eng., 109, pp. 677–690. [CrossRef]
Meylan, M. H., and Squire, V. A., 1996, “Response of a Circular Ice-Floe to Ocean Waves,” J. Geophys. Res., 101(C4), pp. 8869–8884. [CrossRef]
Keller, J. B., 1998, “Gravity Waves on Ice-Covered Water,” J. Geophys., 103(C4), pp. 7663–7669. [CrossRef]
Squire, V. A., and Dixon, T. W., 2001, “On Modelling an Iceberg Embedded in Shore-Fast Sea Ice,” J. Eng. Math., 40(3), pp. 211–226. [CrossRef]
Sahoo, T., Yip, T. L., and Chwang, A. T., 2001, “Scattering of Surface Waves by a Semi-Infinite Floating Elastic Plate,” Phys. Fluids, 13(11), pp. 3215–3222. [CrossRef]
Evans, D. V., and Porter, R., 2003, “Wave Scattering by Narrow Cracks in Ice Sheets Floating on Water of Finite Depth,” J. Fluid Mech., 484, pp. 143–165. [CrossRef]
Kagemoto, H., and Yue, D. K., 1986, “Interactions Among Multiple Three-Dimensional Bodies in Water Waves: An Exact Algebraic Method,” J. Fluid Mech., 166, pp. 189–209. [CrossRef]
Peter, M. A., and Meylan, M. H., 2004, “Infinite-Depth Interaction Theory for Arbitrary Floating Bodies Applied to Wave Forcing of Ice Floes,” J. Fluid Mech., 500, pp. 145–167. [CrossRef]
Chung, H., and Linton, C.M., 2003, “Interaction Between Water Waves and Elastic Plates: Using the Residue Calculus Technique,” Proceedings of the 18th International Workshop on Water Waves and Floating Bodies, France, Apr. 6–9, pp. 37–40.
Ohkusu, M., and Namba, Y., 2004, “Hydroelastic Analysis of a Large Floating Structure,” J. Fluids Struct., 19(4), pp. 543–555. [CrossRef]
Athanassoulis, M. A., and Belibassakis, K., 2009, “A Novel Coupled-Mode Theory With Application to Hydroelastic Analysis of Thick, Non-Uniform Floating Bodies Over General Bathymetry,” J. Eng. Marit. Environ., 223(3), pp. 419–438.
Mondal, R., Mohanty, S. K., and Sahoo, T., 2011, “Expansion Formulae for Wave Structure Interaction Problems in Three Dimensions,” IMA J. Appl. Math., 78(2), pp. 181–205. [CrossRef]
Karmakar, D., and Guedes Soares, C., 2012, “Scattering of Gravity Waves by a Moored Finite Floating Elastic Plate,” Appl. Ocean Res., 34, pp. 135–149. [CrossRef]
Ertekin, R. C., and Xia, D., 2014, “Hydroelastic Response of a Floating Runway to Cnoidal Waves,” Phys. Fluids, 26(2), pp. 1–16. [CrossRef]
Papathanasiou, T. K., and Belibassakis, K. A., 2014, “Hydroelastic Analysis of Very Large Floating Structures Based on Modal Expansions and FEM,” Proceedings of the International Conference on Theoretical Mechanics and Applied Mechanics, Venice, Italy, Mar. 15-17, pp. 17–24.
Zhao, C., Hao, X., Liang, R., and Lu, J., 2015, “Influence of Hinged Conditions on the Hydroelastic Response of Compound Floating Structures,” Ocean Eng., 101, pp. 12–24. [CrossRef]
Mindlin, R. D., 1951, “Influence of Rotary Inertia and Shear on Flexural Motion of Isotropic Elastic Plates,” ASME J. Appl. Mech. 18(1), pp. 31–38.
Fox, C., and Squire, V. A., 1991, “Coupling Between the Ocean and an Ice Shelf,” Ann. Glaciol., 15, pp. 101–108. [CrossRef]
Balmforth, N. J., and Craster, R. V., 1999, “Ocean Waves and Ice Sheets,” J. Fluid Mech., 395, pp. 89–124. [CrossRef]
Karmakar, D., and Sahoo, T., 2006, “Flexural Gravity Wavemaker Problem-Revisited,” Fluid Mechanics in Industry and Environment, B. S. Dandapat and B. S. Majumder, eds., Research Publishing Services, Singapore, pp. 285–291.
Karmakar, D., Bhattacharjee, J., and Sahoo, T., 2009, “Wave Interaction With Multiple Articulated Floating Elastic Plates,” J. Fluids Struct., 25(6), pp. 1065–1078. [CrossRef]
Gao, R. P., Tay, Z. Y., Wang, C. M., and Koh, C. G., 2011, “Hydroelastic Response of Very Large Floating Structure With a Flexible Line Connection,” Ocean Eng., 38(17–18), pp. 1957–1966. [CrossRef]
Tay, Z. Y., and Wang, C. M., 2012, “Reducing Hydroelastic Response of Very Large Floating Structures by Altering Their Plan Shapes,” Ocean Syst. Eng., 2(1), pp. 69–81. [CrossRef]
Gao, R. P., Wang, C. M., and Koh, C. G., 2013, “Reducing Hydroelastic Response of Pontoon-Type Very Large Floating Structures Using Flexible Connector and Gill Cells,” Eng. Struct., 52, pp. 372–383. [CrossRef]
Praveen, K. M., Karmakar, D., and Nasar, T., 2016, “Hydroelastic Analysis of Floating Elastic Thick Plate in Shallow Water Depth,” Perspect. Sci. (Elsevier), 8, pp. 770–772. [CrossRef]
Praveen, K. M., Karmakar, D., and Guedes Soares, C., 2018, “Hydroelastic Analysis of Articulated Floating Elastic Plate Based on Timoshenko-Mindlin Plate Theory,” Ships Offshore Struct., 13(S1), pp. 287–301.
Karmakar, D., Bhattacharjee, J., and Sahoo, T., 2007, “Expansion Formulae for Wave Structure Interaction Problems With Applications in Hydroelasticity,” Int. J. Eng. Sci., 45(10), pp. 807–828. [CrossRef]
Wang, C. D., and Meylan, M. H., 2002, “The Linear Wave Response of a Floating Thin Plate on Water of Variable Depth,” Appl. Ocean Res., 24(3), pp. 163–174. [CrossRef]

Figures

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Fig. 1

Schematic diagram for floating elastic plate

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Fig. 2

Contour plot of roots for the plate covered dispersion relation considering k10h = 5, E = 5 GPa, d/L = 0.05, and h/L = 1.0 for finite water depth

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Fig. 3

Contour plot of roots for the plate covered dispersion relation considering k10h = 5, E = 5 GPa, d/L = 0.05, and h/L = 0.5 for shallow water depth

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Fig. 4

Convergence of the reflection and transmission coefficients for the number of evanescent modes, N

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Fig. 5

Validation of reflection coefficient along the plate length considering rotary inertia I = 0 and shear deformation S = 0 with Wang and Meylan [34]

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Fig. 6

Transmission coefficient versus nondimensional wavenumber k10h for different values of (a) plate thickness d/L for h/L = 0.15 and (b) water depths h/L for d/L = 0.02

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Fig. 7

(a) Normalized plate deflection ζ2/I0 and (b) strain along the plate length x/L for different values of plate thickness considering k10h = 5 and h/L = 0.15

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Fig. 8

Nondimensional (a) bending moment M′(x) and (b) shear force W′(x) along the plate length x/L for different values of plate thickness considering k10h = 5 and h/L = 0.15

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Fig. 9

Transmission coefficient versus nondimensional wavenumber k10h for different values of (a) plate thickness d/L for h/L = 0.1 and (b) water depths h/L for d/L = 0.02

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Fig. 10

(a) Normalized plate deflection ζ2/I0 and (b) strain along the plate length x/L for different values of plate thickness considering k10h = 10 and h/L = 0.1

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Fig. 11

Nondimensional (a) bending moment M′(x) and (b) shear force W′(x) along the plate length x/L for different values of plate thickness considering k10h = 10 and h/L = 0.1

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Fig. 12

(a) Reflection and (b) transmission coefficients versus nondimensional wavenumber k10h considering d/L = 0.25 and h/L = 1.0

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Fig. 13

(a) Normalized plate deflection ζ2/I0 and (b) wave-induced strain along the plate length x/L considering k10h = 20.0, d/L = 0.05, and h/L = 0.20

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Fig. 14

Nondimensional (a) bending moment M′(x) and (b) shear force W′(x) along the plate length x/L considering k10h = 20.0, d/L = 0.05, and h/L = 0.20

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Fig. 15

Comparison of (a) reflection and (b) transmission coefficient versus nondimensional wavenumber for finite and shallow water depths varying d/L

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