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Interaction of surface water waves with a vertical elastic plate: a hypersingular integral equation approach

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Abstract

In this paper, we present an alternative method to investigate scattering of water waves by a submerged thin vertical elastic plate in the context of linear theory. The plate is submerged either in deep water or in the water of uniform finite depth. Using the condition on the plate, together with the end conditions, the derivative of the velocity potential in the direction of normal to the plate is expressed in terms of a Green’s function. This expression is compared with that obtained by employing Green’s integral theorem to the scattered velocity potential and the Green’s function for the fluid region. This produces a hypersingular integral equation of the first kind in the difference in potential across the plate. The reflection coefficients are computed using the solution of the hypersingular integral equation. We find good agreement when the results for these quantities are compared with those for a vertical elastic plate and submerged and partially immersed rigid plates. New results for the hydrodynamic force on the plate, the shear stress and the shear strain of the vertical elastic plate are also evaluated and represented graphically.

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    Rumpa Chakraborty

  2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, 721302, India

    Arpita Mondal & R. Gayen

Authors
  1. Rumpa Chakraborty
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  2. Arpita Mondal
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  3. R. Gayen
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Correspondence to R. Gayen.

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Chakraborty, R., Mondal, A. & Gayen, R. Interaction of surface water waves with a vertical elastic plate: a hypersingular integral equation approach. Z. Angew. Math. Phys. 67, 115 (2016). https://doi.org/10.1007/s00033-016-0709-0

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  • DOI: https://doi.org/10.1007/s00033-016-0709-0

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