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Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

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Abstract

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

    Aloknath Chakrabarti

  2. Department of Mathematics, Institute of Chemical Technology, Mumbai, 400019, India

    Smrutiranjan Mohapatra

Authors
  1. Aloknath Chakrabarti
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  2. Smrutiranjan Mohapatra
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Corresponding author

Correspondence to Smrutiranjan Mohapatra.

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Aloknath Chakrabarti is a NASI (National Academy of Science, India) Platinum Jubilee Senior Scientist in the Department of Mathematics, Indian Institute of Science, Bangalore, India. His research interests include boundary value problems, integral equations, diffraction theory and numerical methods. He has about 175 research publications to his credit and is involved in a number of sponsored projects.

Smrutiranjan Mohapatra received his PhD from the Indian Institute of Technology, Guwahati, India in 2009. He also worked as a post doctoral fellow at the Indian Institute of Science, Bangalore, India, prior to accepting his present position of Assistant Professor in the Department of Mathematics, Institute of Chemical Technology Mumbai, India. His main areas of interest are water wave scattering and two-layer fluid. He has 10 research publications to his credit.

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Chakrabarti, A., Mohapatra, S. Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth. J. Marine. Sci. Appl. 12, 325–333 (2013). https://doi.org/10.1007/s11804-013-1204-z

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  • DOI: https://doi.org/10.1007/s11804-013-1204-z

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