Skip to main content
SpringerLink
Log in

Water wave scattering by an elastic thin vertical plate submerged in finite depth water

  • Research Papers
  • Published:
Journal of Marine Science and Application Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • 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.

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  MATH  MathSciNet  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  MATH  Google Scholar 

  • 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.

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India

    Rumpa Chakraborty & B. N. Mandal

Authors
  1. Rumpa Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. N. Mandal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. N. Mandal.

Additional information

Rumpa Chakraborty was born in 1985. She is working as a Senior Research Fellow at the Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India. Her current research interests include water wave problems.

B.N. Mandal was born in 1943. He is a NASIPlatinum Jubilee Senior Scientist at the Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India. His current research interests include water wave problems and associated mathematical techniques, Integral equations, Integral expansions, etc.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chakraborty, R., Mandal, B.N. Water wave scattering by an elastic thin vertical plate submerged in finite depth water. J. Marine. Sci. Appl. 12, 393–399 (2013). https://doi.org/10.1007/s11804-013-1209-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11804-013-1209-7

Keywords

Search

Navigation