The mathematical challenges and modelling of hydroelasticity

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 369, Issue 1947, 2011, Pages 2803-2812

  Korobkin, Alexander ^a   Pǎrǎu, Emilian I ^a   Vanden Broeck, Jean Marc ^b  

^a UNIVERSITY OF EAST ANGLIA   (United Kingdom)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Hydroelasticity; Ice; Slamming; Waves

Indexed keywords

ELASTIC BODY; ELASTIC THEORY; HYDRODYNAMIC EXCITATION; MATHEMATICAL PROBLEMS; TECHNIQUES USED;

DEFORMATION; HYDROELASTICITY; MATHEMATICAL TECHNIQUES;

HYDRODYNAMICS;

EDITORIAL; ELASTICITY; HYDRODYNAMICS; MATHEMATICAL PHENOMENA; THEORETICAL MODEL;

ELASTICITY; HYDRODYNAMICS; MATHEMATICAL CONCEPTS; MODELS, THEORETICAL;

EID: 79960479698     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2011.0116     Document Type: Review

References (48)

1. Squire, V. A. 2007 Of ocean waves and sea-ice revisited. Cold Region Sci. Technol. 49, 110-133. (doi:10.1016/j.coldregions.2007.04.007) (Pubitemid 46865673)
2. Malenica, Š., Senjanović, I., Tomašević, S. & Stumpf, E. 2007 Some aspects of hydroelastic issues in the design of ultra large container ships. In Proc. 22nd IWWWFB, Plitvice, Croatia, 15-18 April 2007, pp. 133-136.
3. Chai, Y. T. & Varyani, K. S. 2006 An absolute coordinate formulation for three-dimensional flexible pipe analysis. Ocean Eng. 33, 23-58. (doi:10.1016/j.oceaneng.2005.04.006) (Pubitemid 41614507)
4. Malenica, Š., Korobkin, A., Scolan, Y.-M., Gueret, R., Delafosse, V., Gazzola, T., Mravak, Z., Chen, X.-B. & Zalar, M. 2006 Hydroelastic impacts in the tanks of LNG carriers. In Proc. 4th Int. Conf. Hydroelasticity in Marine Technology, Wuxi, China, 10-14 September 2006. Beijing, China: National Defence Industry Press.
5. Squire, V. A. 2008 Synergies between VLFS hydroelasticity and sea ice research. Int. J. Offshore Polar Eng. 18, 1-13.
6. Ashton, G. D. 1986 River and lake ice engineering. Littleton, CO:Water Resources Publications.
7. Takizawa, T. 1985 Deflection of a floating sea ice sheet induced by a moving load. Cold Regions Sci. Tech. 11, 171-180. (doi:10.1016/0165-232X(85) 90015-1) (Pubitemid 15586546)
8. Squire, V. A., Hosking, W. H. & Langhorne, P. J. 1996 Moving loads on ice plates. Dordrecht, The Netherlands, Kluwer.
9. P̌ařau, E. & Dias, F. 2002 Nonlinear effects in the response of a floating ice plate to a moving load. J. Fluid Mech. 460, 281-305. (doi:10.1017/S0022112002008236)
10. Toland, J. F. 2008 Steady periodic hydroelastic waves. Arch. Ration. Mech. Anal. 189, 325-362. (doi:10.1007/s00205-007-0104-2)
11. Hegarty, G. M. & Squire, V. A. 2008 A boundary-integral method for the interaction of largeamplitude ocean waves with a compliant floating raft such as a sea-ice floe. J. Eng. Math. 62, 355-372. (doi:10.1007/s10665-008-9219- 1)
12. Chen, X.-J., Wu, Y.-X., Cui, W.-D. & Jensen, J. J. 2006 Review of hydroelasticity theories for global response of marine structures. Ocean Eng. 33, 439-457. (doi:10.1016/j.oceaneng. 2004.04.010) (Pubitemid 43045879)
13. Eatock Taylor, R. 2007 Hydroelasticity of plates and some approximations. J. Eng. Math. 58, 267-278. (doi:10.1007/s10665-006-9121-7) (Pubitemid 47023376)
14. Xia, D., Ertekin, R. C. & Kim, J. W. 2008 Fluid-structure interaction between a two dimensional mat-type VLFS and solitary waves by the Green-Naghdi theory. J. Fluids Struct. 24, 527-540. (doi:10.1016/j.jfluidstructs.2007.10.009)
15. Korobkin, A. A. & Khabakhpasheva, T. I. 2006 Regular wave impact onto an elastic plate. J. Eng. Math. 55, 127-150. (doi:10.1007/s10665-005-0191-8) (Pubitemid 44445961)
16. Kim, Y., Shin, Y. S. & Lee, K. H. 2004 Numerical study of slosh-induced impact pressures on 3D prismatic tank. Appl. Ocean Res. 26, 213-226. (doi:10.1016/j.apor.2005.03.004) (Pubitemid 41226776)
17. Faltinsen, O. M. & Timokha, A. N. 2009 Sloshing. Cambridge, UK: Cambridge University Press.
18. Chatjigeorgiou, I. K. 2008 Application of the WKB method to catenary-shaped slender structures. Math. Comp. Model. 48, 249-257. (doi:10.1016/j.mcm.2007.08.012) (Pubitemid 351672231)
19. Bishop, R. E. D. & Price, W. G. 1979 Hydroelasticity of ships. Cambridge, UK: Cambridge University Press.
20. Chen, X., Wu, Y., Cui, W. & Tang, X. 2003 Non-linear hydroelastic analysis of a moored floating body. Ocean Eng. 20, 965-1003. (doi:10.1016/S0029-8018(02)00078-1) (Pubitemid 36294689)
21. Abrahams, I. D. 1981 Scattering of sound by a heavily loaded finite elastic plate. Proc. R. Soc. Lond. A 378, 89-117. (doi:10.1098/rspa.1981.0143) (Pubitemid 12438632)
22. Abrahams, I. D. & Wickham, G. R. 2001 On transient oscillations of plates in moving fluids. Wave Motion 33, 7-24. (doi:10.1016/S0165-2125(00)00060- 3)
23. Peake, N. 2001 Nonlinear stability of a fluid-loaded elastic plate with mean flow. J. Fluid Mech. 434, 101-118. (doi:10.1017/S0022112001003573) (Pubitemid 32454078)
24. Peake, N. & Sorokin, S. V. 2006 A nonlinear model of the dynamics of a large elastic plate with heavy fluid loading. Proc. R. Soc. A 462, 2205-2224. (doi:10.1098/rspa.2006.1673) (Pubitemid 44922044)
25. Eloy, C., Souilliez, C. & Schouveiler, L. 2007 Flutter of a rectangular plate. J. Fluids Struct. 23, 904-919. (doi:10.1016/j.jfluidstructs. 2007.02.002) (Pubitemid 47099475)
26. de Langre, E. 2002 Absolutely unstable waves in inviscid hydroelastic systems. J. Sound Vibr. 256, 299-317. (doi:10.1006/jsvi.2001.4210) (Pubitemid 35427756)
27. Chambolle, A., Desjardins, B., Esteban, M. J. & Grandmont, C. 2005 Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate. J. Math. Fluid Mech. 7, 368-404. (doi:10.1007/s00021-004- 0121-y) (Pubitemid 41203777)
28. Coutand, D. & Shkoller, S. 2005 Motion of an elastic solid inside an incompressible viscous fluid. Arch. Ration. Mech. Anal. 176, 25-102. (doi:10.1007/s00205-004-0340-7) (Pubitemid 40550137)
29. Coutand, D. & Shkoller, S. 2006 The interaction between quasilinear elastodynamics and the Navier-Stokes equations. Arch. Ration. Mech. Anal. 179, 303-352. (doi:10.1007/s00205-005-0385-2) (Pubitemid 43052185)
30. San Martin, J., Scheid, J.-F., Takahashi, T. & Tucsnak, M. 2008 An initial and boundary value problem modeling fish-like swimming. Arch. Ration. Mech. Anal. 188, 429-455. (doi:10.1007/ s00205-007-0092-2)
31. Squire, V. A. 2011 Past, present and impendent hydroelastic challenges in the polar and subpolar seas. Phil. Trans. R. Soc. A 369, 2813-2831. (doi:10.1098/rsta.2011.0093)
32. Brocklehurst, P., Korobkin, A. & P̌ařau, E. I. 2011 Hydroelastic wave diffraction by a vertical cylinder. Phil. Trans. R. Soc. A 369, 2832-2851. (doi:10.1098/rsta.2011.0110)
33. Avital, E. J. & Miloh, T. 2011 Sound scattering by free surface piercing and fluid-loaded cylindrical shells. Phil. Trans. R. Soc. A 369, 2852-2863. (doi:10.1098/rsta.2011.0098)
34. Favrie, N. & Gavrilyuk, S. 2011 Mathematical and numerical model for nonlinear viscoplasticity. Phil. Trans. R. Soc. A 369, 2864-2880. (doi:10.1098/rsta.2011.0099)
35. Gudmestad, O. T. 2011 Transient motions of an oscillating system caused by forcing terms proportional to the velocity of the structural motion. Phil. Trans. R. Soc. A 369, 2881-2891. (doi:10.1098/rsta.2011.0107)
36. Kapsenberg, G. K. 2011 Slamming of ships: where are we now? Phil. Trans. R. Soc. A 369, 2892-2919. (doi:10.1098/rsta.2011.0118)
37. Ten, I., Malenica, Š. & Korobkin, A. 2011 Semi-analytical models of hydroelastic sloshing impact in tanks of liquefied natural gas vessels. Phil. Trans. R. Soc. A 369, 2920-2941. (doi:10.1098/rsta.2011.0112)
38. Plotnikov, P. I. & Toland, J. F. 2011 Modelling nonlinear hydroelastic waves. Phil. Trans. R. Soc. A 369, 2942-2956. (doi:10.1098/rsta. 2011.0104)
39. Vanden-Broeck, J.-M. & P̌ařau, E. I. 2011 Two-dimensional generalized solitary waves and periodic waves under an ice sheet. Phil. Trans. R. Soc. A 369, 2957-2972. (doi:10.1098/rsta.2011.0108)
40. Forbes, L. K. 1988 Surface waves of large amplitude beneath an elastic sheet. II. Galerkin solution. J. Fluid Mech. 188, 491-508. (doi:10.1017/ S0022112088000813)
41. Bonnefoy, F., Meylan, M. H. & Ferrant, P. 2009 Nonlinear higher-order spectral solution for a two-dimensional moving load on ice. J. Fluid Mech. 621, 215-242. (doi:10.1017/S002211 2008004849)
42. P̌ařau, E. I. & Vanden-Broeck, J.-M. 2011 Three-dimensional waves beneath an ice sheet due to a steadily moving pressure. Phil. Trans. R. Soc. A 369, 2973-2988. (doi:10.1098/rsta.2011.0115)
43. Rayleigh, L. 1883 The form of standing waves on the surface of running water. Proc. Lond. Math. Soc. 15, 69-78. (doi:10.1112/plms/s1-15.1.69)
44. Davys, J. W., Hosking, R. J. & Sneyd, A. D. 1985 Waves due to a steadily moving source on a floating ice plate. J. Fluid Mech. 158, 269-287. (doi:10.1017/S0022112085002646) (Pubitemid 15581378)
45. Milinazzo, F. A., Shinbrot, M. & Evans, N. W. 1995 A mathematical analysis of the steady response of floating ice to the uniform motion of a rectangular load. J. Fluid Mech. 287, 173-197. (doi:10.1017/S0022112095000917)
46. Whittaker, R. J., Heil, M. & Waters, S. L. 2011 The energetics of flow through a rapidly oscillating tube with slowly varying amplitude. Phil. Trans. R. Soc. A 369, 2989-3006. (doi:10.1098/rsta.2011.0106)
47. Whittaker, R. J., Waters, S. L., Jensen, O. E., Boyle, J. & Heil, M. 2010 The energetics of flow through a rapidly oscillating tube. I. General theory. J. Fluid Mech. 648, 83-121. (doi:10.1017/ S0022112009992904)
48. Smith, F. T. & Wilson, P. L. 2011 Fluid-body interactions: clashing, skimming, bouncing. Phil. Trans. R. Soc. A 369, 3007-3024. (doi:10.1098/rsta. 2011.0092)