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

• Published in: International journal of mechanical sciences Vol. 133; pp. 260 - 272
• Main Authors: Chatjigeorgiou, Ioannis K., Korobkin, Alexander A., Cooker, Mark J.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-11-2017
• Subjects: Elliptical harmonics; Integral equations; Mixed boundary value problems; Pressure-impulse; Steep wave impact; Triple trigonometrical series; Mixed boundary value problems; Elliptical harmonics; Integral equations; Steep wave impact; Pressure-impulse; Triple trigonometrical series
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2017.08.045

•The three-dimensional hydrodynamic slamming problem on a vertical plate subjected to the impact of a steep wave using linear potential theory is considered.•The problem is complicated by assuming a rectangular opening on the plate.•The examined configuration determines two boundary value problems with mixed conditions.•The mathematical process assimilates the plate with a degenerate elliptical cylinder allowing the employment of elliptical harmonics.•The theory is extended to the computation of the total impulse exerted on the plate using pressure-impulse theory.
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.
(a) The leading order potential during the impact of a steep wave on a vertical plate with an open rectangular section, (b) The first-order potential during the impact of a steep wave on a vertical plate with an open rectangular section. [Display omitted]