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Journal of Engineering Mathematics

, Volume 116, Issue 1, pp 49–72 | Cite as

Effect of a floating permeable plate on the hydroelastic response of a very large floating structure

  • S. Singla
  • T. SahooEmail author
  • S. C. Martha
  • H. Behera
Article
  • 18 Downloads

Abstract

The effectiveness of a floating porous plate for mitigating the wave-induced structural response of a very large floating structure is investigated using the eigenfunction expansion method. The analysis is based on the assumption of a small-amplitude structural response of the very large floating structure and the linearized theory of water waves with the assumption that the elastic plate is floating freely on the free surface. The elastic plate is modeled using thin plate theory, and the wave past the porous plate is based on the assumptions of the generalized porous wavemaker theory. The horizontal plate reflects and dissipates a major part of the wave energy, which in turn reduces the wave-induced structural response of the structure. Wave reflection and dissipation increase in an oscillatory manner with an increase in the wavenumber associated with the incident wave, and a complementary trend is observed in the wave transmission, with the oscillatory trend diminishing for higher values of structural porosity. When the distance between the porous plate and floating elastic plate is an integer multiple of half the wavelength, a certain periodic oscillatory pattern occurs in the wave reflection, with complementary patterns being observed in the wave transmission and dissipation. The amplitude of the periodic oscillatory pattern in the wave reflection reduces with an increase in the length of the porous plate of moderate porosity. Moreover, the wave energy reflection and dissipation are greater in case of short compared with long waves for a floating porous plate of larger length. The elastic plate deflection and free surface elevation on the lee side of the floating elastic plate attenuate with an increase in the length of the porous plate for a moderate value of the structural porosity. The reflection coefficient and forces acting on the plate follow a similar pattern with variation of the distance between the porous plate and large floating structure, whilst the shear force and strain acting on the floating structure are complementary to the wave reflection and forces acting on the porous plate.

Keywords

Dissipation coefficient Eigenfunction matching Horizontal porous plate Reflection coefficient Transmission coefficient Water wave scattering 

Notes

Acknowledgements

S.C.M. gratefully acknowledges the Department of Science and Technology (DST), Government of India for financial support (grant no. SB/FTP/MS-034/2013). S.S. is grateful to the CTS visitors program for her visit to IIT Kharagpur in December 2017, during which this work was initiated.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoparRupnagarIndia
  2. 2.Department of Ocean Engineering and Naval ArchitectureIndian Institute of Technology KharagpurKharagpurIndia
  3. 3.Department of MathematicsSRM Institute of Science and Technology, KattankulathurChennaiIndia

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