Mathematical study on the potential flow past a vertical submerged flexible plate of non-uniform thickness

Abstract

The present work emphasizes on the mathematical study of two-dimensional potential fluid flow past a vertical flexible plate of non-uniform thickness submerged in a water domain of finite depth. The boundary value problem associated with the described model is solved by two mathematical techniques while considering Kirchhoff’s thin plate theory. The first method is based on a perturbation analysis involving a small parameter ϵ, while the second method directly employs the classical method of integration and Green’s integral theorem to the governing equations to obtain the solution. Both the techniques result into two different systems of integral equations which are solved numerically using appropriate approximations. It has been established numerically that for smaller thickness variations depicted by particular values of ϵ (ϵ≤0.001), the two methods yield the same numerical results for all the hydrodynamic quantities. The correctness of the present results is verified by comparing them graphically with the ones already existing in the literature. Effects of the non-uniform plate thickness on various hydrodynamic parameters are presented graphically by choosing various thickness profiles. Also, comparisons are made with the results of constant thickness elastic plate to distinguish its hydrodynamic behaviour from the one having non-uniform thickness.