Abstract
The problem of the behavior of a floating elastic strip-shaped plate in waves is considered. A new numerical method for solving this problem based on the Wiener-Hopf technique is proposed. The solution of the boundary value problem is reduced to an infinite system of linear algebraic equations which satisfies the reduction conditions. The calculation results are compared both with experiment and with the calculations of other authors. In the case of short incident waves the system of equations obtained can be essentially simplified. Three short-wave approximations are proposed, namely, the single-mode, four-mode and uniform approximations, which ensure good agreement with calculations based on the complete model. Simple explicit formulas are obtained for the single-mode and uniform approximations.
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REFERENCES
I.V. Sturova, "Oblique surface waves incidence on an elastic strip," Zh. Prikl. Mekh. Tekh. Fiz., 40, No. 4, 62 (1999).
T. I. Khabakhpasheva, "Plane problem of an elastic floating plate," in: Continuum Dynamics, Vol. 116 [in Russian], Izd. In-ta Gidrodinamiki SO RAN, Novosibirsk (2000), p. 166.
A.A. Korobkin, "Numerical and asymptotic investigation of the plane problem of the hydroelastic behavior of a floating plate in waves," Zh. Prikl. Mekh. Tekh. Fiz., 41, No. 2, 90 (2000).
M. Meylan and V. A. Squire, "The response of ice floes to ocean waves," J. Geophys. Res., 99, No. C1, 891 (1994).
A. E. Bukatov and D.D. Zav'yalov, "Impingement of surface waves on the edge of compressed ice," Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 3, 121 (1995).
C. Fox and V.A. Squire, "Reflection and transmission characteristics at the edge of short fast sea ice," J. Geophys. Res., 95, No. C7, 11629 (1990).
C. Wu, E. Watanabe, and T. Utsunomiay, "An eigenfunction expansion-matching method for analyzing the wave-induced responses of an elastic floating plate," Appl. Ocean Res., 17, No. 5, 301 (1995).
K. Yago, S. Ohmatsu, and H. Endo, "On the hydroelastic response of box-shaped floating structure with shallow draft," J. Soc. Naval Architects Japan, 182, 307 (1997).
D.V. Evans and T.V. Davies, Wave-Ice Interaction, Davidson Lab., Stevens Inst. Technol., Rep. No. 1313, New Jersey (1968).
V.V. Varlamov, "Scattering of internal waves at the edge of an elastic plate," Zh. Vychisl. Matematiki i Mat. Fiziki, 25, 413 (1985).
R.V. Gol'dshtein and A.V. Marchenko, "Plane gravity wave diffraction at the edge of an ice sheet," Prikl. Mat. Mekh., 53, 924 (1989).
N. J. Balmforth and R.V. Craster, "Ocean waves and ice sheets," J. Fluid Mech., 395, 89 (1999).
L.A. Tkacheva, "Scattering of surface waves by the edge of a floating elastic plate," Zh. Prikl. Mekh. Tekh. Fiz., 42, No. 4, 88 (2001).
L. A. Tkacheva, "Surface wave diffraction on a floating elastic plate," Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 121 (2001).
B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations, Pergamon Press, London (1958).
I. M. Gel'fand and G. E. Shilov, Distributions and Operations on Them [in Russian], Fizmatgiz, Moscow (1959).
L.V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).
M. Meylan, V.A. Squire, "Finite-wave reflection and transmission coefficients from a semi-infinite model," J. Geophys. Res. 98, No. C7, 12537 (1993).
I.V. Lavrenov and A.V. Novakov, "Numerical simulation of the interaction between gravity waves and elastic ice floes," Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 3, 123 (2000).
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Tkacheva, L.A. Plane Problem of Surface Wave Diffraction on a Floating Elastic Plate. Fluid Dynamics 38, 465–481 (2003). https://doi.org/10.1023/A:1025106408548
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DOI: https://doi.org/10.1023/A:1025106408548