Convergence Analysis of Havelock-Type Eigenfunction Expansions for Hydroelastic Problems in Water having Infinite Depth

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Authors

  • Santanu Koley
     ,IN

DOI:

https://doi.org/10.18311/jims/2022/25870

Keywords:

Havelock-Type Expansion, Eigenfunctions, Green’s Function, Convergence Analysis.
Applied Mathematics, 34L10, 65N80.

Abstract

The present paper demonstrates the point-wise convergence of the Havelock-type eigenfunction expansion to the velocity potentials associated with the water waves interaction with flexible plate and membranes in water having infinite depth. To consider the higher-order boundary condition at the mean free surface of the water domain, flexible plate and membranes are assumed to float in the mean water level. In the convergence analysis procedure,  firstly, the havelock-type eigenfunction expansion for the unknown velocity potentials associated with the physical problems are obtained. Hereafter, a suitable  Green's function is developed for the associated physical problem. Using the developed Green's function and the associated properties, the vertical components of the Havelock-type eigenfunction expansion is expressed in terms of the Dirac delta function. Finally, using appropriate properties of the Dirac delta function, the point-wise convergence of the Havelock-type eigenfunction expansion is demonstrated.

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Published

2022-08-23

How to Cite

Koley, S. (2022). Convergence Analysis of Havelock-Type Eigenfunction Expansions for Hydroelastic Problems in Water having Infinite Depth. The Journal of the Indian Mathematical Society, 89(3-4), 333–340. https://doi.org/10.18311/jims/2022/25870

Issue

Volume 89, Issue 3-4, July-December 2022

Section

Articles

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Copyright (c) 2022 Santanu Koley

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2020-08-12
Accepted 2022-02-17
Published 2022-08-23

 

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