TY - JOUR
AU - Koley, Santanu
PY - 2022/08/23
Y2 - 2022/12/02
TI - Convergence Analysis of Havelock-Type Eigenfunction Expansions for Hydroelastic Problems in Water having Infinite Depth
JF - The Journal of the Indian Mathematical Society
JA - JIMS
VL - 89
IS - 3-4
SE - Articles
DO - 10.18311/jims/2022/25870
UR - https://informaticsjournals.com/index.php/jims/article/view/25870
SP - 333-340
AB - <div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>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.</span></p></div></div></div>
ER -