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Advances in Mathematical Physics
Volume 2015, Article ID 308318, 11 pages
http://dx.doi.org/10.1155/2015/308318
Research Article

The Nonlinear Hydroelastic Response of a Semi-Infinite Elastic Plate Floating on a Fluid due to Incident Progressive Waves

1School of Mathematics and Physics, Qingdao University of Science and Technology, 99 Songling Road, Qingdao 266061, China
2Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 149 Yanchang Road, Shanghai 200072, China

Received 26 October 2014; Revised 25 February 2015; Accepted 4 March 2015

Academic Editor: Klaus Kirsten

Copyright © 2015 Ping Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. G. Greenhill, “Wave motion in hydrodynamics,” The American Journal of Mathematics, vol. 9, no. 1, pp. 62–96, 1886. View at Publisher · View at Google Scholar · View at MathSciNet
  2. D. V. Evans and T. V. Davies, “Wave-ice interaction,” Tech. Rep., DTIC Document, 1968. View at Google Scholar
  3. C. Fox and V. A. Squire, “On the oblique reflexion and transmission of ocean waves at shore fast sea ice,” Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, vol. 347, no. 1682, pp. 185–218, 1994. View at Publisher · View at Google Scholar · View at Scopus
  4. C. Fox and V. A. Squire, “Reflection and transmission characteristics at the edge of shore fast sea ice,” Journal of Geophysical Research: Oceans, vol. 95, no. C7, pp. 11629–11639, 1990. View at Publisher · View at Google Scholar
  5. V. A. Squire, J. P. Dugan, P. Wadhams, P. J. Rottier, and A. K. Liu, “Of ocean waves and sea ice,” Annual Review of Fluid Mechanics, vol. 27, no. 1, pp. 115–168, 1995. View at Publisher · View at Google Scholar · View at Scopus
  6. T. Sahoo, T. Yip, A. T. Chwang et al., “On the interaction of surface waves with a semi-infinite elastic plate,” in Proceedings of the 10th International Offshore and Polar Engineering Conference, International Society of Offshore and Polar Engineers, 2000.
  7. B. Teng, L. Cheng, S. X. Liu, and F. J. Li, “Modified eigenfunction expansion methods for interaction of water waves with a semi-infinite elastic plate,” Applied Ocean Research, vol. 23, no. 6, pp. 357–368, 2001. View at Publisher · View at Google Scholar · View at Scopus
  8. F. Xu and D. Q. Lu, “An optimization of eigenfunction expansion method for the interaction of water waves with an elastic plate,” Journal of Hydrodynamics, vol. 21, no. 4, pp. 526–530, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. Q. Lin and D. Q. Lu, “Hydroelastic interaction between obliquely incident waves and a semi-infinite elastic plate on a two-layer fluid,” Applied Ocean Research, vol. 43, pp. 71–79, 2013. View at Publisher · View at Google Scholar · View at Scopus
  10. L. K. Forbes, “Surface waves of large amplitude beneath an elastic sheet. Part 1. High-order series solution,” Journal of Fluid Mechanics, vol. 169, pp. 409–428, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  11. L. K. Forbes, “Surface waves of large amplitude beneath an elastic sheet. Part 2. Galerkin solution,” Journal of Fluid Mechanics, vol. 188, pp. 491–508, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J.-M. Vanden-Broeck and E. I. Părău, “Two-dimensional generalized solitary waves and periodic waves under an ice sheet,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 369, no. 1947, pp. 2957–2972, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. P. A. Milewski, J.-M. Vanden-Broeck, and Z. Wang, “Hydroelastic solitary waves in deep water,” Journal of Fluid Mechanics, vol. 679, pp. 628–640, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. S. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems [Ph.D. thesis], Shanghai Jiao Tong University, Shanghai, China, 1992.
  15. S.-J. Liao, “On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1274–1303, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  16. D. Xu, Z. Lin, S. Liao, and M. Stiassnie, “On the steady-state fully resonant progressive waves in water of finite depth,” Journal of Fluid Mechanics, vol. 710, pp. 379–418, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. P. Wang and D. Lu, “Analytic approximation to nonlinear hydroelastic waves traveling in a thin elastic plate floating on a fluid,” Science China Physics, Mechanics and Astronomy, vol. 56, no. 11, pp. 2170–2177, 2013. View at Publisher · View at Google Scholar · View at Scopus
  18. S. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, vol. 2, CRC Press, Boca Raton, Fla, USA, 2004. View at MathSciNet
  19. S. Liao, Homotopy Analysis Method in Nonlinear Differential Equations, 2012.