Citation:

Rumpa Chakraborty and B. N. Mandal.Water Wave Scattering by an Elastic Thin Vertical Plate Submerged in Finite Depth Water[J].Journal of Marine Science and Application,2013,(4):393-399.[doi:10.1007/s11804-013-1209-7]

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Rumpa Chakraborty and B. N. Mandal.Water Wave Scattering by an Elastic Thin Vertical Plate Submerged in Finite Depth Water[J].Journal of Marine Science and Application,2013,(4):393-399.[doi:10.1007/s11804-013-1209-7]

Water Wave Scattering by an Elastic Thin Vertical Plate Submerged in Finite Depth Water

- Title:
- Water Wave Scattering by an Elastic Thin Vertical Plate Submerged in Finite Depth Water

- Author(s):
- Rumpa Chakraborty and B. N. Mandal

- Affilations:

- Keywords:
- thin vertical elastic plate; uniform finite depth water; wave scattering; reflection and transmission coefficients

- DOI:
- 10.1007/s11804-013-1209-7

- Abstract:
- The problem of water wave scattering by a thin vertical elastic plate submerged in uniform finite depth water is investigated here. The boundary condition on the elastic plate is derived from the Bernoulli-Euler equation of motion satisfied by the plate. Using the Green’s function technique, from this boundary condition, the normal velocity of the plate is expressed in terms of the difference between the velocity potentials (unknown) across the plate. The two ends of the plate are either clamped or free. The reflection and transmission coefficients are obtained in terms of the integrals’ involving combinations of the unknown velocity potential on the two sides of the plate, which satisfy three simultaneous integral equations and are solved numerically. These coefficients are computed numerically for various values of different parameters and depicted graphically against the wave number in a number of figures.

Chakrabarti A (2000). On the solution of the problem of scattering of surface-water waves by the edge of an ice-cover. Proc. Roy. Soc. Lond. A., 457, 1087-1100.

Evans DV (1970). Diffraction of water waves by a submerged vertical plate. J. Fluid Mech., 40,433-451.

Fox C, Squire VA (1994). On the oblique reflection and transmission of ocean waves from shore fast sea ice. Philos. Trans. R. Soc. Lond. A, 347, 185-218.

Gayen R, Mandal BN (2009). Scattering of surface water waves by a floating elastic plate in two dimensions. SIAM J. Appl. Math., 69(6), 1520-1541.

Goswami SK (1983). Scattering of surface waves by a submerged fixed vertical plate in water of finite depth. J. Indian Inst. Sci., 64B, 79-88.

Mandal BN, Dolai DP (1994). Oblique water wave diffraction by thin vertical barriers in water of uniform finite depth. Appl. Ocean Res., 16(4), 195-203 .

Mandal BN, Gayen R (2006).Water wave scattering by bottom undulations in the presence of a thin partially immersed barrier. Appl. Ocean Res., 28, 113-119.

Meylan M (1995). A reflexible vertical sheet in waves. Int. J. Offshore and Polar Engng., 5, 105-110.

Meylan MH, Hassan MU, Peter MA (2009). Water waves scattering by submerged elastic plates. Q. JI Mech. Appl. Math., 62(3), 321-344 .

Peter MA, Meylan MH, Chung H (2004). Wave scattering by a circular elastic plate in water of finite depth. Int. J. Off. Polar Engg., 14(1), 1-5.

Porter R, Evans DV (1995). Complementary approximation to wave scattering by vertical barriers. J. Fluid Mech., 249, 155-180.

Sahoo T, Yip TL, Chwang AT (2001). Scattering of surface waves by a semi-infinite floating elastic plate. Phys. Fluids, 13(11), 3215-3222.

Stoker JJ (1957). Water waves. Intersicence Publishers, New York, 430-449.

Sturova IV (2003). The action of an unsteady load on a circular elastic plate floating on shallow water. J. Appl Math. Mech., 67, 407-416.

Sturova IV (2006a). The effect of periodic surface pressure on a rectangular elastic plate floating on shallow water. J. Appl. Math. Mech., 70, 378-386.

Sturova IV (2006b). Unsteady behavior of an elastic beam floating on the surface of an infinitely deep fluid. J. Appl. Mech. Tech. Phys., 47, 71-78.

Taylor AB (1986). Mathematical models in applied mechanics. Clarendon Press, Oxford, 122-128.

Ursell F (1947). The effect of a fixed vertical barrier on surface waves in deep water. Proc. Camb. Phil. Soc., 43, 374-382.

- Memo:
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Last Update:
2013-11-14