# Three-dimensional steep wave impact on a vertical plate with an open rectangular section

Chatzigeorgiou, Ioannis, Korobkin, Alexander ORCID: https://orcid.org/0000-0003-3605-8450 and Cooker, Mark (2017) Three-dimensional steep wave impact on a vertical plate with an open rectangular section. International Journal of Mechanical Sciences, 133. pp. 260-272. ISSN 0020-7403

## Abstract

The present study treats the three-dimensional hydrodynamic slamming problem on a vertical plate subjected to the impact of a steep wave moving towards the plate with a constant velocity. The problem is complicated significantly by assuming that there is a rectangular opening on the plate which allows a discharge of the liquid. The analysis is conducted analytically assuming linear potential theory. The examined configuration determines two boundary value problems with mixed conditions which fully are taken into account. The mathematical process assimilates the plate with a degenerate elliptical cylinder allowing the employment of elliptical harmonics that ensure the satisfaction of the free-surface boundary condition of the front face of the steep wave, away from the plate. This assumption leads to an additional boundary value problem with mixed conditions in the vertical direction. The associated problem involves triple trigonometrical series and it is solved through a transformation into integral equations. To tackle the boundary value problem in the vertical direction a perturbation technique is employed. Extensive numerical calculations are presented as regards the variation of the velocity potential on the plate at the instant of the impact which reveals the influence of the opening. The theory is extended to the computation of the total impulse exerted on the plate using pressure-impulse theory.

Item Type: Article Note added 4.2.19, it was only today that I saw the acceptance data of this joint paper: accepted 21.8.17, and DOI: 10.1016/j.ijmecsci.2017.08.045 . Further, I noticed a mistake in the journal title, now correced from "Engineering" to "Mechanical". steep wave impact,pressure-impulse,elliptical harmonics,mixed boundary value problems,triple trigonometrical series,integral equations Faculty of Science > School of Mathematics Faculty of Science > Research Groups > Fluid and Solid MechanicsFaculty of Science > Research Groups > Centre for Interdisciplinary Mathematical Research (former - to 2017) Pure Connector 26 Aug 2017 05:05 22 Oct 2022 02:43 https://ueaeprints.uea.ac.uk/id/eprint/64673 10.1016/j.ijmecsci.2017.08.045