Hydroelastic interaction between water waves and a thin elastic plate of arbitrary geometry

  • Feng Xu
  • DongQiang Lu
Research Paper


An analytical method is developed for the hydroelastic interaction between surface incident waves and a thin elastic plate of arbitrary geometry floating on an inviscid fluid of finite depth in the framework of linear potential flow. Three kinds of edge conditions are considered and the corresponding analytical representations are derived in the polar coordinate system. According to the surface boundary conditions, the fluid domain is divided into two regions, namely, an open water region and a plate-covered region. With the assumption that all the motion is time-harmonic, the series solutions for the spatial velocity potentials are derived by the method of eigenfunction expansion. The matching conditions for the continuities of the velocity and pressure are transformed by taking the inner products successively with respect to the vertical eigenfunction for the free surface and the angular eigenfunction. A system of simultaneous equations, including two edge conditions and two matching conditions, is set up for deriving the expansion coefficients. As an example, numerical computation for the expansion coefficients of truncated series is performed for an elliptic plate. The results show that the method suggested here is useful to revealing the physical features of the gravity wave scattering in the open water and the hydroelastic response in the plate.


wave scattering method of matched eigenfunction expansions elastic plate arbitrary geometry hydroelastic response 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kashiwagi M. Research on hydroelastic responses of VLFS: Recent progress and future work. Int J Offshore Polar Eng, 2000, 10(2): 81–90Google Scholar
  2. 2.
    Watanabe E, Utsunomiya T, Wang C M. Hydroelastic analysis of pontoon-type VLFS: A literature survey. Eng Struct, 2004, 26(2): 245–256CrossRefGoogle Scholar
  3. 3.
    Ohmatsu S. Overview: Research on wave loading and responses of VLFS. Mar Struct, 2005, 18(2): 149–168CrossRefGoogle Scholar
  4. 4.
    Chen X J, Wu Y S, Cui WC, et al. Review of hydroelasticity theories for global response of marine structures. Ocean Eng, 2006, 33(3–4): 439–457CrossRefGoogle Scholar
  5. 5.
    Cui W C, Yang J M, Wu Y S, et al. Theory of Hydroelasticity and its Application to Very Large Floating structures. Shanghai: Shanghai Jiao Tong University Press, 2007Google Scholar
  6. 6.
    Squire V A. Of ocean waves and sea-ice revisited. Cold Regions Sci Tech, 2007, 49(2): 110–133CrossRefGoogle Scholar
  7. 7.
    Squire V A. Synergies between VLFS hydroelasticity and sea ice research. Int J Offshore Polar Eng, 2008, 18(4): 241–253MathSciNetGoogle Scholar
  8. 8.
    Jiao L L, Fu S X, Wang C, et al. Comparison of approaches for the hydroelastic response analysis of Very Large Floating Structures. J Ship Mech, 2006, 10(3): 71–91Google Scholar
  9. 9.
    Sahoo T, Yip T L, Chwang A T. Scattering of surface waves by a semiinfinite floating elastic plate. Phys Fluids, 2001, 13(11): 3215–3222CrossRefADSGoogle Scholar
  10. 10.
    Teng B, Cheng L, Li S X, et al. Modified eigenfunction expression methods for interaction of water waves with a semi-infinite elastic plate. Appl Ocean Res, 2001, 23(6): 357–368CrossRefGoogle Scholar
  11. 11.
    Xu F, Lu D Q. An optimization of eigenfunction expansion method for the interaction of water waves with an elastic plate. J Hydrodyn, 2009, 21(4): 526–530CrossRefGoogle Scholar
  12. 12.
    Meylan M H. Spectral solution of time-dependent shallaw water hydroelasticity. J Fluid Mech, 2002, 454: 387–402zbMATHCrossRefADSGoogle Scholar
  13. 13.
    Fox C, Squire V A. On the oblique reflexion and transmission of ocean waves at shore fast sea ice. Phil Trans R Soc Lond A, 1994, 347: 185–218zbMATHCrossRefADSGoogle Scholar
  14. 14.
    Meylan M H. Wave response of an ice floe of arbitrary geometry. J Geophys Res-Oceans, 2002, 107(C1): 3005CrossRefMathSciNetADSGoogle Scholar
  15. 15.
    Qiu L C, Liu H. Three-dimensional time-domain analysis of very large floating structures subjected to unsteady external loading. J Offshore Mech Arctic Eng, 2007, 129(1): 21–28CrossRefMathSciNetGoogle Scholar
  16. 16.
    Zilman G, Miloh T. Hydroelastic buoyant circular plate in shallow water: A closed form solution. Appl Ocean Res, 2000, 22(4): 191–198CrossRefGoogle Scholar
  17. 17.
    Peter M A, Meylan M H, Chung H. Wave scattering by a circular elastic plate in water of finite depth: Closed form solution. Int J Offshore Polar Eng, 2004, 14(2): 81–85Google Scholar
  18. 18.
    Lu D Q, Dai S Q. Flexural- and capillary-gravity waves due to fundamental singularities in an inviscid fluid of finite depth. Int J Eng Sci, 2008, 46(11): 1183–1193CrossRefMathSciNetzbMATHGoogle Scholar
  19. 19.
    Timoshenko S, Woinowsky-Krieger S. Theory of Plates and Shells. 2nd ed. Singapore: McGraw-Hill, 1970. 87–88Google Scholar
  20. 20.
    Zhou D. An exact method of bending of elastic thin plates with arbitrary shape. Appl Math Mech-Engl Ed, 1996, 17(12): 1189–1192zbMATHCrossRefGoogle Scholar
  21. 21.
    Lu D Q, Dai S Q. Generation of transient waves by impulsive disturbances in an inviscid fluid with an ice-cover. Arch Appl Mech, 2006, 76(1–2): 49–63zbMATHCrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina
  2. 2.Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghaiChina

Personalised recommendations